We survey the literature on those variants of the {\em chromatic number\/} problem where not
only a proper coloring has to be found (ie, adjacent vertices must not receive the same color) …

In this paper we survey results and open problems on the structure of additive and
hereditary properties of graphs. The important role of vertex partition problems, in particular …

While solving a question on the list coloring of planar graphs, Dvořák and Postle introduced
the new notion of DP-coloring (they called it correspondence coloring). A DP-coloring of a …

Dvořák and Postle introduced DP‐coloring of simple graphs as a generalization of list‐
coloring. They proved a Brooks' type theorem for DP‐coloring; and Bernshteyn, Kostochka …

We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and
extensions of each. The proofs illustrate some of the major techniques in graph coloring …

Correspondence coloring, or DP‐coloring, is a generalization of list coloring introduced
recently by Dvořák and Postle [11]. In this article, we establish a version of Dirac's theorem …

New trends in the theory of graph colorings : Choosability and list coloring Page 1 New trends
in the theory of graph colorings : Choosability and list coloring Jan Kratochv l Zsolt Tuzay Margit …

Brooks’ Theorem via the Alon–Tarsi Theorem - ScienceDirect Skip to main contentSkip to
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It is proved that the choice number of every graph G embedded on a surface of Euler genus
ε≥ 1 and ε≠ 3 is at most the Heawood number H(ϵ)=⌊(7+24ϵ+1)/2⌋ and that the equality …

A classical theorem of Gallai states that in every graph that is critical for k-colorings, the
vertices of degree k-1 induce a tree-like graph whose blocks are either complete graphs or …