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arXiv · 2606.31702

List-Coloring and Chromatic-Choosability -- A Dynamic Survey

Nandana K Vasudevan·K Somasundaram·N Narayanan
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Abstract

List-coloring, introduced independently by Vizing and by Erd\H{o}s, Rubin, and Taylor in the 1970s, generalizes ordinary vertex coloring by assigning to each vertex its own set of admissible colors. A graph is chromatic-choosable if its list chromatic number equals its chromatic number. The previous survey on list-coloring by D R Woodall (2001), emphasized defective choosability, the list-coloring conjectures, and different methods used for list-coloring. This survey reviews major developments on list-coloring and chromatic-choosability, with emphasis on graph classes for which equality is known, graph classes exhibiting a nontrivial gap, and the principal methods used to prove such results. The survey covers embedded graphs, perfect graphs, complete bipartite and multipartite graphs, claw-free graphs, line graphs, powers of graphs, graph products, and selected variants of list-coloring.

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Nandana K Vasudevan, K Somasundaram, N Narayanan. 2026-06-30. List-Coloring and Chromatic-Choosability -- A Dynamic Survey. https://arxiv.org/abs/2606.31702

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