The smallest integer k needed for the assignment of k colors to the elements so that the
coloring is proper (vertices and edges) is called the total chromatic number of a graph …

A vertex coloring of a graph is said to be conflict-free with respect to neighborhoods if for
every non-isolated vertex there is a color appearing exactly once in its (open) neighborhood …

arXiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arXiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …

Graph Searching Games and Probabilistic Methods is the first book that focuses on the
intersection of graph searching games and probabilistic methods. The book explores …

The discharging method is a powerful proof technique, especially for graph coloring
problems. Its major downside is that it often requires lengthy case analyses, which are …

The notion of $ S $-labeling, where $ S $ is a subset of the symmetric group, is a common
generalization of signed $ k $-coloring, signed $\mathbb {Z} _k $-coloring, DP-coloring …

We prove that every connected plane graph of given girth g and minimum degree at least 2
contains an edge whose degrees are bounded from above by one of the pairs (2, 5) or (3, 3) …

Twin-width is a graph parameter, which has recently been introduced by Bonnet, Kim,
Thomassé and Watrigant [13, 14] and further developed in particular in [5–11], also see [28] …

A graph G is called (d 1,…, dr)-colorable if its vertex set can be partitioned into r sets V 1,…,
V r such that the maximum degree of the induced subgraph G [V i] of G is at most di for …

Wegner conjectured that if G is a planar graph with maximum degree Δ≥ 8, then χ (G 2)≤ 3
2 Δ+ 1. This problem has received much attention, but remains open for all Δ≥ 8. Here we …