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arXiv · 2305.10108

List 3-Coloring on Comb-Convex and Caterpillar-Convex Bipartite Graphs

Banu Baklan Şen·Öznur Yaşar Diner·Thomas Erlebach
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Abstract

Given a graph $G=(V, E)$ and a list of available colors $L(v)$ for each vertex $v\in V$, where $L(v) \subseteq \{1, 2, \ldots, k\}$, List $k$-Coloring refers to the problem of assigning colors to the vertices of $G$ so that each vertex receives a color from its own list and no two neighboring vertices receive the same color. The decision version of the problem List $3$-Coloring is NP-complete even for bipartite graphs, and its complexity on comb-convex bipartite graphs has been an open problem. We give a polynomial-time algorithm to solve List $3$-Coloring for caterpillar-convex bipartite graphs, a superclass of comb-convex bipartite graphs. We also give a polynomial-time recognition algorithm for the class of caterpillar-convex bipartite graphs.

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Banu Baklan Şen, Öznur Yaşar Diner, Thomas Erlebach. 2023-12-13. List 3-Coloring on Comb-Convex and Caterpillar-Convex Bipartite Graphs. https://doi.org/10.1007/978-3-031-49190-0_12

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