Random Structures and Algorithms最新文献

{"title":"The square of a Hamilton cycle in randomly perturbed graphs","authors":"Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia, Jozef Skokan","doi":"10.1002/rsa.21215","DOIUrl":"https://doi.org/10.1002/rsa.21215","url":null,"abstract":"We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given <span data-altimg=\"/cms/asset/2a01f103-ed02-475c-9849-35ae2fdcdde2/rsa21215-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"8\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21215-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,8\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"element\" data-semantic-speech=\"alpha element of left parenthesis 0 comma 1 right parenthesis\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,∈\" data-semantic-parent=\"9\" data-semantic-role=\"element\" data-semantic-type=\"operator\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"7\" data-semantic-content=\"2,6\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"3,4,5\" data-semantic-content=\"4\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"7\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\" rspace=\"3\" style=\"margin-left: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21215:rsa21215-math-0001\" display=\"inline\" location=\"graphic/rsa21215-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,8\" data-semantic-content=\"1\" data-semantic-role=\"element\" data-semantic-speech=\"alpha element of left parenthesis 0 comma 1 right parenthesis\" data-semantic-type=\"infixop\"><mi ","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transference for loose Hamilton cycles in random 3-uniform hypergraphs","authors":"Kalina Petrova, Miloš Trujić","doi":"10.1002/rsa.21216","DOIUrl":"https://doi.org/10.1002/rsa.21216","url":null,"abstract":"A loose Hamilton cycle in a hypergraph is a cyclic sequence of edges covering all vertices in which only every two consecutive edges intersect and do so in exactly one vertex. With Dirac's theorem in mind, it is natural to ask what minimum <span data-altimg=\"/cms/asset/96bf6800-4a53-4fcf-aa7b-a11ff802fdc1/rsa21216-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"1746\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21216-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"d\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21216:rsa21216-math-0001\" display=\"inline\" location=\"graphic/rsa21216-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"d\" data-semantic-type=\"identifier\">d</mi></mrow>$$ d $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>-degree condition guarantees the existence of a loose Hamilton cycle in a <span data-altimg=\"/cms/asset/e14262ab-ac20-4578-be3f-bbe30fc08b73/rsa21216-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"1747\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21216-math-0002.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"k\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21216:rsa21216-math-0002\" display=\"inline\" location=\"graphic/rsa21216-math-0002.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"k\" data-semantic-type=\"identifier\">k</mi></mrow>$$ k $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>-uniform hypergraph. For <span data-altimg=\"/cms/asset/03c2dae8-8d2b-4c90-a6ec-2587395b51ad/rsa21216-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"1748\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21216-math-0003.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The hitting time of clique factors","authors":"Annika Heckel, Marc Kaufmann, Noela Müller, Matija Pasch","doi":"10.1002/rsa.21218","DOIUrl":"https://doi.org/10.1002/rsa.21218","url":null,"abstract":"In [Trans. Am. Math. Soc. 375 (2022), no. 1, 627–668], Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let <span data-altimg=\"/cms/asset/7b4fb8d9-d0bb-4887-b2d9-9622142ef5ee/rsa21218-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"1925\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21218-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"inequality\" data-semantic-speech=\"r greater than or slanted equals 3\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,⩾\" data-semantic-parent=\"3\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21218:rsa21218-math-0001\" display=\"inline\" location=\"graphic/rsa21218-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic-role=\"inequality\" data-semantic-speech=\"r greater than or slanted equals 3\" data-semantic-type=\"relseq\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">r</mi><mo data-semantic-=\"\" data-semantic-operator=\"relseq,⩾\" data-semantic-parent=\"3\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\">⩾</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\">3</mn></mrow>$$ rgeqslant 3 $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> and let <span data-altimg=\"/cms/asset/30e5ceff-d56d-4eb6-b13d-70f6602bea8e/rsa21218-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"1926\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21218-math-0002.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></m","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weight distribution of random linear codes and Krawtchouk polynomials","authors":"Alex Samorodnitsky","doi":"10.1002/rsa.21214","DOIUrl":"https://doi.org/10.1002/rsa.21214","url":null,"abstract":"For <mjx-container aria-label=\"0 less than lamda less than 1\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,2,4\" data-semantic-content=\"1,3\" data-semantic- data-semantic-role=\"inequality\" data-semantic-speech=\"0 less than lamda less than 1\" data-semantic-type=\"relseq\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"relseq,&lt;\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,&lt;\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"/cms/asset/0b6af63e-f89a-49ec-8e43-239794a37806/rsa21214-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,2,4\" data-semantic-content=\"1,3\" data-semantic-role=\"inequality\" data-semantic-speech=\"0 less than lamda less than 1\" data-semantic-type=\"relseq\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\">0</mn><mo data-semantic-=\"\" data-semantic-operator=\"relseq,&lt;\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\">&lt;</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">λ</mi><mo data-semantic-=\"\" data-semantic-operator=\"relseq,&lt;\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\">&lt;</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn></mrow>$$ 0&lt;lambda &lt;1 $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> and <mjx-container aria-label=\"n right arrow infinity\" ctxtmenu_counter=\"1\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-e","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"367 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A polynomial-time approximation scheme for the maximal overlap of two independent Erdős–Rényi graphs","authors":"Jian Ding, Hang Du, Shuyang Gong","doi":"10.1002/rsa.21212","DOIUrl":"https://doi.org/10.1002/rsa.21212","url":null,"abstract":"For two independent Erdős–Rényi graphs <mjx-container aria-label=\"bold upper G left parenthesis n comma p right parenthesis\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,7\" data-semantic-content=\"8,0\" data-semantic- data-semantic-role=\"simple function\" data-semantic-speech=\"bold upper G left parenthesis n comma p right parenthesis\" data-semantic-type=\"appl\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"9\" data-semantic-role=\"simple function\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"9\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"6\" data-semantic-content=\"1,5\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"7\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"2,3,4\" data-semantic-content=\"3\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"6\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\" rspace=\"3\" style=\"margin-left: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"7\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"/cms/asset/2faa26af-1d72-4b99-9369-f9fefb9bf168/rsa21212-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,7\" data-semantic-content=\"8,0\" data-semantic-role=\"simple function\" data-semantic-speech=\"bold upper G left parenthesis n comma p right parenthesis\" data-semantic-type=\"appl\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Isoperimetric inequalities for real-valued functions with applications to monotonicity testing","authors":"Hadley Black, Iden Kalemaj, Sofya Raskhodnikova","doi":"10.1002/rsa.21211","DOIUrl":"https://doi.org/10.1002/rsa.21211","url":null,"abstract":"We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions <mjx-container aria-label=\"f colon StartSet 0 comma 1 EndSet Superscript d Baseline right arrow double struck upper R\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,1,13\" data-semantic-content=\"1\" data-semantic- data-semantic-role=\"sequence\" data-semantic-speech=\"f colon StartSet 0 comma 1 EndSet Superscript d Baseline right arrow double struck upper R\" data-semantic-type=\"punctuated\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"14\" data-semantic-role=\"colon\" data-semantic-type=\"punctuation\" rspace=\"2\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"10,12\" data-semantic-content=\"11\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"arrow\" data-semantic-type=\"relseq\"><mjx-msup data-semantic-children=\"8,9\" data-semantic- data-semantic-parent=\"13\" data-semantic-role=\"set collection\" data-semantic-type=\"superscript\"><mjx-mrow data-semantic-children=\"7\" data-semantic-content=\"2,6\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"set collection\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"3,4,5\" data-semantic-content=\"4\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"7\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\" rspace=\"3\" style=\"margin-left: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow><mjx-script style=\"vertical-align: 0.477em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-s","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weakly saturated random graphs","authors":"Zsolt Bartha, Brett Kolesnik","doi":"10.1002/rsa.21210","DOIUrl":"https://doi.org/10.1002/rsa.21210","url":null,"abstract":"As introduced by Bollobás, a graph <mjx-container aria-label=\"upper G\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper G\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"/cms/asset/11561f75-127e-4f60-9ceb-e40378b00f88/rsa21210-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper G\" data-semantic-type=\"identifier\">G</mi></mrow>$$ G $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is weakly <mjx-container aria-label=\"upper H\" ctxtmenu_counter=\"1\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"/cms/asset/19810fb2-a72c-4618-af37-9f48b522a70f/rsa21210-math-0002.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H\" data-semantic-type=\"identifier\">H</mi></mrow>$$ H $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>-saturated if the complete graph <mjx-container aria-label=\"upper K Subscript n\" ctxtmenu_counter=\"2\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper K Subscript n\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.04em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi>","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On pattern-avoiding permutons","authors":"Frederik Garbe, Jan Hladký, Gábor Kun, Kristýna Pekárková","doi":"10.1002/rsa.21208","DOIUrl":"https://doi.org/10.1002/rsa.21208","url":null,"abstract":"The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order <math altimg=\"urn:x-wiley:rsa:media:rsa21208:rsa21208-math-0001\" display=\"inline\" location=\"graphic/rsa21208-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>k</mi>\u0000</mrow>\u0000$$ k $$</annotation>\u0000</semantics></math> have a particularly simple structure. Namely, almost every fiber of the disintegration of the permuton (say, along the x-axis) consists only of atoms, at most <math altimg=\"urn:x-wiley:rsa:media:rsa21208:rsa21208-math-0002\" display=\"inline\" location=\"graphic/rsa21208-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mo stretchy=\"false\">(</mo>\u0000<mi>k</mi>\u0000<mo form=\"prefix\">−</mo>\u0000<mn>1</mn>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ left(k-1right) $$</annotation>\u0000</semantics></math> many, and this bound is sharp. We use this to give a simple proof of the “permutation removal lemma.”","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139667155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupling Bertoin's and Aldous–Pitman's representations of the additive coalescent","authors":"Igor Kortchemski, Paul Thévenin","doi":"10.1002/rsa.21206","DOIUrl":"https://doi.org/10.1002/rsa.21206","url":null,"abstract":"We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous and Pitman, involves the components obtained by logging the Brownian continuum random tree (CRT) by a Poissonian rain on its skeleton as time increases. The second one, due to Bertoin, involves the excursions above its running infimum of a linear-drifted standard Brownian excursion as its drift decreases. Our main tool is the use of an exploration algorithm of the so-called cut-tree of the Brownian CRT, which is a tree that encodes the genealogy of the fragmentation of the CRT.","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139465102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cycles with many chords","authors":"Nemanja Draganić, Abhishek Methuku, David Munhá Correia, Benny Sudakov","doi":"10.1002/rsa.21207","DOIUrl":"https://doi.org/10.1002/rsa.21207","url":null,"abstract":"How many edges in an <mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21207-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21207:rsa21207-math-0001\" display=\"inline\" location=\"graphic/rsa21207-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\">n</mi></mrow>$$ n $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>-vertex graph will force the existence of a cycle with as many chords as it has vertices? Almost 30 years ago, Chen, Erdős and Staton considered this question and showed that any <mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"1\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21207-math-0002.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:rsa:media:rsa21207:rsa21207-math-0002\" display=\"inline\" location=\"graphic/rsa21207-math-0002.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\">n</mi></mrow>$$ n $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>-vertex graph with <mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"2\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/rsa21207-math-0003.png\"><mjx-semantics><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,6\" data-semantic-content=\"7\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"2 n Superscript 3 divided by 2\" data-semantic-type=\"","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}