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arXiv · 2006.03009

List-three-coloring $ P_t $-free graphs with no induced 1-subdivision of $ K_{1,s} $

Maria Chudnovsky·Sophie Spirkl·Mingxian Zhong
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Abstract

Let $s$ and $t$ be positive integers. We use $P_t$ to denote the path with $t$ vertices and $K_{1,s}$ to denote the complete bipartite graph with parts of size $1$ and $s$ respectively. The one-subdivision of $K_{1,s}$ is obtained by replacing every edge $\{u,v\}$ of $K_{1,s}$ by two edges $\{u,w\}$ and $\{v,w\}$ with a new vertex $w$. In this paper, we give a polynomial-time algorithm for the list-three-coloring problem restricted to the class of $P_t$-free graph with no induced 1-subdivision of $K_{1,s}$.

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Maria Chudnovsky, Sophie Spirkl, Mingxian Zhong. 2020-06-04. List-three-coloring $ P_t $-free graphs with no induced 1-subdivision of $ K_{1,s} $. https://arxiv.org/abs/2006.03009

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