Intersection Graphs of Maximal Sub-polygons of k-Lizards

被引：0

作者：

Daugherty, Caroline ^{[1
]}

Laison, Joshua D. ^{[2
]}

Robinson, Rebecca ^{[3
]}

Salois, Kyle ^{[4
]}

机构：

[1] MIT, Operat Res Ctr, Cambridge, MA USA

[2] Willamette Univ, Math Dept, Salem, OR 97301 USA

[3] Univ Colorado Denver, Math & Stat Sci Dept, Denver, CO USA

[4] Colorado State Univ, Math Dept, Ft Collins, CO USA

来源：

GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 04期

关键词：

Intersection graph; MSP graph;

D O I：

10.1007/s00373-023-02670-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce k-maximal sub-polygon graphs (k-MSP graphs), the intersection graphs of maximal polygons contained in a polygon with sides parallel to a regular 2k-gon. We prove that all complete graphs are k-MSP graphs for all k > 1; trees are 2-MSP graphs; trees are k-MSP graphs for k > 2 if and only if they are caterpillars; and n-cycles are not k-MSP graphs for n > 3 and k > 1. We derive bounds for which j cycles appear as induced subgraphs of k-MSP graphs. As our main result, we construct examples of graphs which are k-MSP graphs and not j-MSP graphs for all k > 1, j > 1, k not equal j.

引用

页数：16

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