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.
The locating-chromatic number of a graph combines proper vertex coloring with vertex identification through distances to color classes. Although this parameter has been studied for many graph families, general results for bipartite graphs remain limited. Bipartite graphs contain structural symmetries, especially within...
Dian Kastika Syofyan, E. Baskoro, H. Assiyatun et al.· Baghdad Science Journal· 0 citations
An r-dynamic coloring of a graph G is a proper vertex coloring in which each vertex sees at least min{r, d(v)} distinct colors in its neighborhood. The minimum number of colors in such a coloring is the r-dynamic chromatic number χdr(G). We determine exact values and upper bounds of χdr for several graph classes, inclu...
Juan Gutiérrez, Grover Ugarte· Anais do XI Encontro de Teor...· 0 citations
A b-coloring is a proper vertex coloring such that every color class contains a vertex, a so-called b-vertex, which sees all colors in its closed neighborhood. This type of coloring has been intensively studied from both structural and algorithmic point of view. Recently, Zaker [DAM 2025] introduced the notion of a b*-...
In the
flexible list coloring
problem, we consider a graph and a color list assignment on , as well as a subset for which each has a preferred color . Our goal is to find a proper ‐coloring of such that for at least vertices . We say that is ‐flexibly ‐choosable if for every ‐size list assignment on and every sub...
Richard Bi, Peter Bradshaw· Journal of Graph Theory· 0 citations
We give an explicit simple bridgeless cubic graph on 112 vertices with no Petersen coloring, and hence no normal 5-edge-coloring. The graph is identified by the SHA-256 digest in Theorem 1.1. It is assembled from three copies of a four-pole L and a claw six-pole C; in turn, L is assembled from four copies of a four-pol...
Recently, Chudnovsky, Cook, Davies, Oum, and Tan obtained the first finite bound on the chromatic number of t-perfect graphs, showing that they are 199053-colorable. We improve this bound to 186 by refining their proof. The original proof establishes that every graph with large odd girth and large chromatic number cont...
Matija Novakovi'c, Stefan Weltge· 0 citations
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