Journal of Graph Theory最新文献

The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-08 DOI: 10.1002/jgt.23208

Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier

{"title":"The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest","authors":"Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier","doi":"10.1002/jgt.23208","DOIUrl":"https://doi.org/10.1002/jgt.23208","url":null,"abstract":"<div>\u0000 \u0000 Deciding whether a graph can be edge-decomposed into a matching and a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0001\" wiley:location=\"equation/jgt23208-math-0001.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-bounded linear forest was recently shown by Campbell, Hörsch, and Moore to be nonedeterministic Polynomial time (NP)-complete for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>9</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0002\" wiley:location=\"equation/jgt23208-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>9</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>, and solvable in polynomial time for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0003\" wiley:location=\"equation/jgt23208-math-0003.png\"><mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. In the first part of this paper, we close this gap by showing that this problem is NP-complete for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0004\" wiley:location=\"equation/jgt23208-math-0004.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>3</mn>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"76-87"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Maximal Degrees in Subgraphs of Kneser Graphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-08 DOI: 10.1002/jgt.23213

Peter Frankl, Andrey Kupavskii

{"title":"Maximal Degrees in Subgraphs of Kneser Graphs","authors":"Peter Frankl, Andrey Kupavskii","doi":"10.1002/jgt.23213","DOIUrl":"https://doi.org/10.1002/jgt.23213","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we study the maximum degree in nonempty-induced subgraphs of the Kneser graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>KG</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0001\" wiley:location=\"equation/jgt23213-math-0001.png\"><mrow><mrow><mi>KG</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math>. One of the main results asserts that, for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0002\" wiley:location=\"equation/jgt23213-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x0003E}</mo><msub><mi>k</mi><mn>0</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>64</mn>\u0000 \u0000 <msup>\u0000 <mi>k</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0003\" wiley:location=\"equation/jgt23213-math-0003.png\"><mrow><mrow><mi>n</mi><mo>unicode{x0003E}</mo><mn>64</mn><msup><mi>k</mi><mn>2</mn></msup></mrow></mrow></math></annotation>\u0000 </semantics></math>, whenever a nonempty subgraph has <sp","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"88-96"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Ubiquity of Oriented Double Rays

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-06 DOI: 10.1002/jgt.23216

Florian Gut, Thilo Krill, Florian Reich

{"title":"On the Ubiquity of Oriented Double Rays","authors":"Florian Gut, Thilo Krill, Florian Reich","doi":"10.1002/jgt.23216","DOIUrl":"https://doi.org/10.1002/jgt.23216","url":null,"abstract":"A digraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0001\" wiley:location=\"equation/jgt23216-math-0001.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is called ubiquitous if every digraph that contains arbitrarily many vertex-disjoint copies of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0002\" wiley:location=\"equation/jgt23216-math-0002.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> also contains infinitely many vertex-disjoint copies of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0003\" wiley:location=\"equation/jgt23216-math-0003.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>. We study oriented double rays, that is, digraphs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0004\" wiley:location=\"equation/jgt23216-math-0004.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> whose underlying undirected graphs are double rays. Calling a vertex of an oriented double ray a turn if it has in-degree or out-degree 2, we prove that an oriented double ray with at least one turn is ubiquitous if and only if it has a (finite) odd number of turns. It remains an open problem to determine whether the consistently oriented double ray is ubiquitous.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"62-67"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23216","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Variant of the Teufl-Wagner Formula and Applications

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-06 DOI: 10.1002/jgt.23220

Danyi Li, Weigen Yan

{"title":"A Variant of the Teufl-Wagner Formula and Applications","authors":"Danyi Li, Weigen Yan","doi":"10.1002/jgt.23220","DOIUrl":"https://doi.org/10.1002/jgt.23220","url":null,"abstract":"<div>\u0000 \u0000 Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23220:jgt23220-math-0001\" wiley:location=\"equation/jgt23220-math-0001.png\"><mrow><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mo>*</mo>\u0000 </msup>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mo>*</mo>\u0000 </msup>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"68-75"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Balanced Independent Sets and Colorings of Hypergraphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-06 DOI: 10.1002/jgt.23212

Abhishek Dhawan

{"title":"Balanced Independent Sets and Colorings of Hypergraphs","authors":"Abhishek Dhawan","doi":"10.1002/jgt.23212","DOIUrl":"https://doi.org/10.1002/jgt.23212","url":null,"abstract":"A <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0001\" wiley:location=\"equation/jgt23212-math-0001.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-uniform hypergraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0002\" wiley:location=\"equation/jgt23212-math-0002.png\"><mrow><mrow><mi>H</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0003\" wiley:location=\"equation/jgt23212-math-0003.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-partite if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0004\" wiley:location=\"equation/jgt23212-math-0004.png\"><mrow><mrow><mi>V</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> can be partitioned into <math>\u0000 <semant","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"43-51"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Packing Colourings in Complete Bipartite Graphs and the Inverse Problem for Correspondence Packing

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-06 DOI: 10.1002/jgt.23215

Stijn Cambie, Rimma Hämäläinen

{"title":"Packing Colourings in Complete Bipartite Graphs and the Inverse Problem for Correspondence Packing","authors":"Stijn Cambie, Rimma Hämäläinen","doi":"10.1002/jgt.23215","DOIUrl":"https://doi.org/10.1002/jgt.23215","url":null,"abstract":"<div>\u0000 \u0000 Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing. However, even for complete bipartite graphs, the list chromatic number can be arbitrarily large, and its exact determination is generally difficult. For the packing variant, this question becomes even harder. In this paper, we study the correspondence- and list-packing numbers of (asymmetric) complete bipartite graphs. In the most asymmetric cases, Latin squares come into play. Our results show that every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>z</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <msup>\u0000 <mi>Z</mi>\u0000 \u0000 <mo>+</mo>\u0000 </msup>\u0000 \u0000 <mo></mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mn>3</mn>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23215:jgt23215-math-0001\" wiley:location=\"equation/jgt23215-math-0001.png\"><mrow><mrow><mi>z</mi><mo>unicode{x02208}</mo><msup><mi mathvariant=\"double-struck\">Z</mi><mo>unicode{x0002B}</mo></msup><mo>unicode{x0005C}</mo><mrow><mo class=\"MathClass-open\">{</mo><mn>3</mn><mo class=\"MathClass-close\">}</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> can be equal to the correspondence packing number of a graph. We disprove a recent conjecture that relates the list packing number and the list flexibility number. Additionally, we improve the threshold functions for the correspondence packing variant.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"52-61"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Weak Rainbow Saturation Numbers of Graphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-01-06 DOI: 10.1002/jgt.23211

Xihe Li, Jie Ma, Tianying Xie

{"title":"Weak Rainbow Saturation Numbers of Graphs","authors":"Xihe Li, Jie Ma, Tianying Xie","doi":"10.1002/jgt.23211","DOIUrl":"https://doi.org/10.1002/jgt.23211","url":null,"abstract":"<div>\u0000 \u0000 For a fixed graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23211:jgt23211-math-0001\" wiley:location=\"equation/jgt23211-math-0001.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>, we say that an edge-colored graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23211:jgt23211-math-0002\" wiley:location=\"equation/jgt23211-math-0002.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is weakly <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23211:jgt23211-math-0003\" wiley:location=\"equation/jgt23211-math-0003.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-rainbow saturated if there exists an ordering <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mi>m</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23211:jgt23211-math-0004\" wiley:location=\"equation/jgt23211-math-0004.png\"><mrow><mrow><msub><mi>e</mi><mn>1</mn></msub><mo>,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>,</mo><mo>unicode{","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"35-42"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Positive Co-Degree Turán Number for C5 and C5−

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-30 DOI: 10.1002/jgt.23206

Zhuo Wu

{"title":"Positive Co-Degree Turán Number for C5 and C5−","authors":"Zhuo Wu","doi":"10.1002/jgt.23206","DOIUrl":"https://doi.org/10.1002/jgt.23206","url":null,"abstract":"The minimum positive co-degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msubsup>\u0000 <mi>δ</mi>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>+</mo>\u0000 </msubsup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23206:jgt23206-math-0001\" wiley:location=\"equation/jgt23206-math-0001.png\"><mrow><mrow><msubsup><mi>unicode{x003B4}</mi><mrow><mi>r</mi><mo>unicode{x02212}</mo><mn>1</mn></mrow><mo>unicode{x0002B}</mo></msubsup><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> of a nonempty <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23206:jgt23206-math-0002\" wiley:location=\"equation/jgt23206-math-0002.png\"><mrow><mrow><mi>r</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23206:jgt23206-math-0003\" wiley:location=\"equation/jgt23206-math-0003.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is the maximum <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt2","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"25-30"},"PeriodicalIF":0.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

C10 Has Positive Turán Density in the Hypercube

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-30 DOI: 10.1002/jgt.23217

Alexandr Grebennikov, João Pedro Marciano

{"title":"C10 Has Positive Turán Density in the Hypercube","authors":"Alexandr Grebennikov, João Pedro Marciano","doi":"10.1002/jgt.23217","DOIUrl":"https://doi.org/10.1002/jgt.23217","url":null,"abstract":"<div>\u0000 \u0000 The <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23217:jgt23217-math-0001\" wiley:location=\"equation/jgt23217-math-0001.png\"><mrow><mrow><mi>n</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-dimensional hypercube <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23217:jgt23217-math-0002\" wiley:location=\"equation/jgt23217-math-0002.png\"><mrow><mrow><msub><mi>Q</mi><mi>n</mi></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> is a graph with vertex set <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>0</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23217:jgt23217-math-0003\" wiley:location=\"equation/jgt23217-math-0003.png\"><mrow><mrow><msup><mrow><mo class=\"MathClass-open\">{</mo><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mo class=\"MathClass-close\">}</mo></mrow><mi>n</mi></msup></mrow></mrow></math></annotation>\u0000 </semantics></math> such that there is an edge between two vertices if and only if they differ in exactly one coordinate. For any graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23217:j","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"31-34"},"PeriodicalIF":0.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extremal Problems for a Matching and Any Other Graph

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-19 DOI: 10.1002/jgt.23210

Xiutao Zhu, Yaojun Chen

{"title":"Extremal Problems for a Matching and Any Other Graph","authors":"Xiutao Zhu, Yaojun Chen","doi":"10.1002/jgt.23210","DOIUrl":"https://doi.org/10.1002/jgt.23210","url":null,"abstract":"<div>\u0000 \u0000 For a family of graphs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23210:jgt23210-math-0001\" wiley:location=\"equation/jgt23210-math-0001.png\"><mrow><mrow><mi class=\"MJX-tex-caligraphic\" mathvariant=\"normal\">unicode{x02131}</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>, a graph is called <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23210:jgt23210-math-0002\" wiley:location=\"equation/jgt23210-math-0002.png\"><mrow><mrow><mi class=\"MJX-tex-caligraphic\" mathvariant=\"normal\">unicode{x02131}</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-free if it does not contain any member of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23210:jgt23210-math-0003\" wiley:location=\"equation/jgt23210-math-0003.png\"><mrow><mrow><mi class=\"MJX-tex-caligraphic\" mathvariant=\"normal\">unicode{x02131}</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> as a subgraph. The generalized Turán number <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>ex</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>r</mi>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23210:jgt23210-math-0004\" wiley:location=\"equation/jgt23210-math-0004.png\"&gt","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"19-24"},"PeriodicalIF":0.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0