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Volumes of Subset Minkowski Sums and the Lyusternik Region 子集Minkowski和的体积与Lyusternik域
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-11-21 DOI: 10.1007/s00454-023-00606-w
Franck Barthe, Mokshay Madiman
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引用次数: 5
Grounded L-Graphs Are Polynomially $$chi $$ -Bounded 接地l -图是多项式$$chi $$有界的
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-11-16 DOI: 10.1007/s00454-023-00592-z
James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak
{"title":"Grounded L-Graphs Are Polynomially $$chi $$ -Bounded","authors":"James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak","doi":"10.1007/s00454-023-00592-z","DOIUrl":"https://doi.org/10.1007/s00454-023-00592-z","url":null,"abstract":"<p>A <i>grounded L-graph</i> is the intersection graph of a collection of “L” shapes whose topmost points belong to a common horizontal line. We prove that every grounded L-graph with clique number <span>(omega )</span> has chromatic number at most <span>(17omega ^4)</span>. This improves the doubly-exponential bound of McGuinness and generalizes the recent result that the class of circle graphs is polynomially <span>(chi )</span>-bounded. We also survey <span>(chi )</span>-boundedness problems for grounded geometric intersection graphs and give a high-level overview of recent techniques to obtain polynomial bounds.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543213","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: 3
Some New Results on Geometric Transversals 关于几何截线的一些新结果
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-11-16 DOI: 10.1007/s00454-023-00573-2
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
{"title":"Some New Results on Geometric Transversals","authors":"Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen","doi":"10.1007/s00454-023-00573-2","DOIUrl":"https://doi.org/10.1007/s00454-023-00573-2","url":null,"abstract":"<p>We investigate a number of questions, problems, and conjectures related to geometric transversal theory. Among our results we disprove a conjecture of Bárány and Kalai regarding weak <span>(varepsilon )</span>-nets for <i>k</i>-flats and convex sets in <span>(mathbb {R}^d)</span>, and we prove a conjecture of Arocha, Bracho, and Montejano regarding a colorful version of the Goodman–Pollack–Wenger transversal theorem. We also investigate the connected components of the space of line transversals to pairwise disjoint convex sets in <span>(mathbb {R}^3)</span>, and we extend a theorem of Karasev and Montejano regarding colorful intersections and <i>k</i>-transversals.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"130 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507782","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: 1
The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions 一组相机的可见体积函数是连续的、分段有理的、局部Lipschitz的和全维半代数的
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-08-12 DOI: 10.1007/s00454-023-00541-w
Jörg Rambau
{"title":"The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions","authors":"Jörg Rambau","doi":"10.1007/s00454-023-00541-w","DOIUrl":"https://doi.org/10.1007/s00454-023-00541-w","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1038 - 1058"},"PeriodicalIF":0.8,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43661006","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
Self-Affine Tiles Generated by a Finite Number of Matrices 有限个矩阵生成的自仿射块
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-23 DOI: 10.1007/s00454-023-00529-6
Guotai Deng, Chuntai Liu, Sze-Man Ngai
{"title":"Self-Affine Tiles Generated by a Finite Number of Matrices","authors":"Guotai Deng, Chuntai Liu, Sze-Man Ngai","doi":"10.1007/s00454-023-00529-6","DOIUrl":"https://doi.org/10.1007/s00454-023-00529-6","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"620 - 644"},"PeriodicalIF":0.8,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47706627","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
Complete Characterization of Polyhedral Self-Affine Tiles 多面体自仿射瓷砖的完全表征
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-19 DOI: 10.1007/s00454-023-00527-8
V. Protasov, T. Zaitseva
{"title":"Complete Characterization of Polyhedral Self-Affine Tiles","authors":"V. Protasov, T. Zaitseva","doi":"10.1007/s00454-023-00527-8","DOIUrl":"https://doi.org/10.1007/s00454-023-00527-8","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"931 - 950"},"PeriodicalIF":0.8,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41753973","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
Uniformly Acute Triangulations of PSLGs PSLG的一致锐角三角剖分
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-08 DOI: 10.1007/s00454-023-00524-x
C. Bishop
{"title":"Uniformly Acute Triangulations of PSLGs","authors":"C. Bishop","doi":"10.1007/s00454-023-00524-x","DOIUrl":"https://doi.org/10.1007/s00454-023-00524-x","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1090 - 1120"},"PeriodicalIF":0.8,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45731652","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: 2
Delaunay and Regular Triangulations as Lexicographic Optimal Chains 作为字典最优链的Delaunay和正则三角剖分
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-05-16 DOI: 10.1007/s00454-023-00485-1
D. Cohen-Steiner, A. Lieutier, J. Vuillamy
{"title":"Delaunay and Regular Triangulations as Lexicographic Optimal Chains","authors":"D. Cohen-Steiner, A. Lieutier, J. Vuillamy","doi":"10.1007/s00454-023-00485-1","DOIUrl":"https://doi.org/10.1007/s00454-023-00485-1","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1 - 50"},"PeriodicalIF":0.8,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45486294","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: 1
Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two 用平移不变的二阶闵可夫斯基张量重构平面椭圆
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-04-03 DOI: 10.1007/s00454-022-00470-0
Rikke Eriksen, Markus Kiderlen
{"title":"Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two","authors":"Rikke Eriksen, Markus Kiderlen","doi":"10.1007/s00454-022-00470-0","DOIUrl":"https://doi.org/10.1007/s00454-022-00470-0","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"69 1","pages":"1095-1120"},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45389334","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: 1
Morphing Triangle Contact Representations of Triangulations 三角形的变形三角形接触表示
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-03-15 DOI: 10.1007/s00454-022-00475-9
Patrizio Angelini, S. Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli
{"title":"Morphing Triangle Contact Representations of Triangulations","authors":"Patrizio Angelini, S. Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli","doi":"10.1007/s00454-022-00475-9","DOIUrl":"https://doi.org/10.1007/s00454-022-00475-9","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"991 - 1024"},"PeriodicalIF":0.8,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48006648","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: 1
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