[HTML][HTML] Colorings of plane graphs: a survey

OV Borodin - Discrete Mathematics, 2013 - Elsevier
After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

Graph coloring with local constraints-A survey

Z Tuza - 1997 - opus4.kobv.de
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) …

The power of multi-step vizing chains

ABG Christiansen - Proceedings of the 55th Annual ACM Symposium on …, 2023 - dl.acm.org
Recent papers have addressed different variants of the (Δ+ 1)-edge-colouring problem by
concatenating or gluing together many Vizing chains to form what Bernshteyn coined multi …

Mr. paint and mrs. correct

U Schauz - the electronic journal of combinatorics, 2009 - combinatorics.org
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 …

[HTML][HTML] Light subgraphs of graphs embedded in the plane—a survey

S Jendrol, HJ Voss - Discrete Mathematics, 2013 - Elsevier
It is well known that every planar graph contains a vertex of degree at most 5. A theorem of
Kotzig states that every 3-connected planar graph contains an edge whose endvertices …

[HTML][HTML] An introduction to the discharging method via graph coloring

DW Cranston, DB West - Discrete Mathematics, 2017 - Elsevier
We provide a “how-to” guide to the use and application of the Discharging Method. Our aim
is not to exhaustively survey results proved by this technique, but rather to demystify the …

Total colorings of planar graphs with large maximum degree

OV Borodin, AV Kostochka… - Journal of graph …, 1997 - Wiley Online Library
Total colorings of planar graphs with large maximum degree Page 1 Total Colorings of Planar
Graphs with Large Maximum Degree OV Borodin,1,* AV Kostochka,2,† and DR Woodall3 1 …

Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)

DW Cranston - arXiv preprint arXiv:2210.05915, 2022 - arxiv.org
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) …

On differences between DP-coloring and list coloring

AY Bernshteyn, AV Kostochka - Siberian Advances in Mathematics, 2019 - Springer
DP-coloring (also known as correspondence coloring) is a generalization of list coloring
introduced recently by Dvořák and Postle [12]. Many known upper bounds for the list …

List colourings of graphs

DR Woodall - London Mathematical Society Lecture Note Series, 2001 - books.google.com
A list colouring of a graph is a colouring in which each vertex v receives a colour from a
prescribed list L (v) of colours. This paper about list colourings can be thought of as being …