This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63
(1995), 153–158), who proved that the list edge chromatic numberχ′ list (G) of a bipartite …

A list channel assignment problem is a triple (G, L, w), where G is a graph, L is a function
which assigns to each vertex of G a list of integers (colors), and w is a function which assigns …

We introduce a coloring game on graphs, in which each vertex $ v $ of a graph $ G $ owns a
stack of $\ell_v {-} 1$ erasers. In each round of this game the first player Mr. Paint takes an …

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 …

In this article we survey the emerging field of descriptive graph combinatorics. This area has
developed in the last two decades or so at the interface of descriptive set theory and graph …

Let G be a graph with a vertex colouring α. Let a and b be two colours. Then a connected
component of the subgraph induced by those vertices coloured either a or b is known as a …

One of the basic results in graph colouring is Brooks' theorem [4] which asserts that the
chromatic number of every connected graph, that is not a complete graph or an odd cycle …

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 …

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if
a path of length two exists between them. In this paper some results on injective colorings of …