Choosability in bounded sequential list coloring

Simone Gama; Rosiane de Freitas; Mário Salvatierra

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arXiv · 1812.11685

Choosability in bounded sequential list coloring

Simone Gama·Rosiane de Freitas·Mário Salvatierra

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Abstract

The list coloring problem is a variation of the classical vertex coloring problem, extensively studied in recent years, where each vertex has a restricted list of allowed colors, and having some variations as the $(\gamma,\mu)$-coloring, where the color lists have sequential values with known lower and upper bounds. This work discusses the choosability property, that consists in determining the least number $k$ for which it has a proper list coloring no matter how one assigns a list of $k$ colors to each vertex. This is a $\Pi_2^P$-complete problem, however, we show that $k$-$(\gamma,\mu)$-choosability is an $NP$-problem due to its relation with the $k$-coloring of a graph and application of methods of proof in choosability for some classes of graphs, such as complete bipartite graph, which is $ 3 $-choosable, but $ 2 $-$(\gamma,\mu)$-choosable.

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Simone Gama, Rosiane de Freitas, Mário Salvatierra. 2018-12-31. Choosability in bounded sequential list coloring. https://arxiv.org/abs/1812.11685

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