接地l -图是多项式$$\chi $$有界的

Pub Date : 2023-11-16 DOI:10.1007/s00454-023-00592-z

James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak

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引用次数: 3

摘要

一个接地L图是“L”形集合的交点图，其顶点属于一条公共水平线。证明了每一个团数为$\omega $的接地l图最多有一个色数$17\omega ^4$。这改进了McGuinness的双指数界，推广了最近关于圆图类是多项式$\chi $有界的结论。我们还研究了接地几何相交图的$\chi $有界性问题，并对获得多项式界的最新技术进行了高级概述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Grounded L-Graphs Are Polynomially $$\chi $$ -Bounded$

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Grounded L-Graphs Are Polynomially $$\chi $$ -Bounded

A grounded L-graph 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 $\omega $ has chromatic number at most $17\omega ^4$. This improves the doubly-exponential bound of McGuinness and generalizes the recent result that the class of circle graphs is polynomially $\chi $-bounded. We also survey $\chi $-boundedness problems for grounded geometric intersection graphs and give a high-level overview of recent techniques to obtain polynomial bounds.

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