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

Source: [List-Coloring and Chromatic-Choosability -- A Dynamic Survey](<https://www.sota2.com/research/paper/6a449f15e0224bd4f49931b9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-02T05:00:13.060Z

Authors: Nandana K Vasudevan, K Somasundaram, N Narayanan

Published: 2026-06-30T14:10:19.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.31702>)

[PDF](<https://arxiv.org/pdf/2606.31702.pdf>)