接地l -图是多项式$$\chi $$有界的

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry 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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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.