List-k-Coloring H-Free Graphs for All $$k>4$$

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2024-05-14 DOI:10.1007/s00493-024-00106-2

Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl

引用次数: 0

Abstract

Given an integer $k>4$ and a graph H, we prove that, assuming P$\ne $ NP, the List-k -Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all $k\ge 1$.

Abstract Image

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针对所有 $$k>4$$ 的列表-k-着色无 H 图

给定一个整数$k>4$和一个图H，我们证明，假设P$\ne $ NP，当且仅当H的每个分量都是最多三个顶点上的路径，或者去除H的孤立顶点会留下一个五顶点路径的诱导子图时，局限于无H图的List-k -Coloring Problem可以在多项式时间内求解。事实上，"如果 "的蕴含对于所有的 $k\ge 1$ 都成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.