scholarly journals List-Coloring the Squares of Planar Graphs without 4-Cycles and 5-Cycles

2016 ◽  
Vol 85 (4) ◽  
pp. 721-737 ◽  
Author(s):  
Daniel W. Cranston ◽  
Bobby Jaeger
Keyword(s):  
Planar Graphs ◽  
List Coloring

scholarly journals 3-list-coloring planar graphs of girth 4

2011 ◽  
Vol 311 (6) ◽  
pp. 413-417 ◽  
Author(s):  
Jun-Lin Guo ◽  
Yue-Li Wang
Keyword(s):  
Planar Graphs ◽  
List Coloring

List coloring triangle‐free planar graphs

2020 ◽  
Vol 94 (2) ◽  
pp. 278-298
Author(s):  
Jianzhang Hu ◽  
Xuding Zhu
Keyword(s):  
Planar Graphs ◽  
List Coloring

scholarly journals 5-list-coloring planar graphs with distant precolored vertices

2017 ◽  
Vol 122 ◽  
pp. 311-352 ◽  
Author(s):  
Zdeněk Dvořák ◽  
Bernard Lidický ◽  
Bojan Mohar ◽  
Luke Postle
Keyword(s):  
Planar Graphs ◽  
List Coloring

Adapted list coloring of planar graphs

2009 ◽  
Vol 62 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Louis Esperet ◽  
Mickaël Montassier ◽  
Xuding Zhu
Keyword(s):  
Planar Graphs ◽  
List Coloring

scholarly journals Distributed Coloring in Sparse Graphs with Fewer Colors

10.37236/8395 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Pierre Aboulker ◽  
Marthe Bonamy ◽  
Nicolas Bousquet ◽  
Louis Esperet
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Distributed Algorithm ◽  
Planar Graphs ◽  
List Coloring ◽  
Sparse Graphs ◽  
Four Color Theorem

This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof gives a (sequential) quadratic algorithm finding such a coloring. A natural problem is to improve this complexity in the distributed setting. Using the fact that planar graphs contain linearly many vertices of degree at most 6, Goldberg, Plotkin, and Shannon obtained a deterministic distributed algorithm coloring $n$-vertex planar graphs with 7 colors in $O(\log n)$ rounds. Here, we show how to color planar graphs with 6 colors in $\text{polylog}(n)$ rounds. Our algorithm indeed works more generally in the list-coloring setting and for sparse graphs (for such graphs we improve by at least one the number of colors resulting from an efficient algorithm of Barenboim and Elkin, at the expense of a slightly worst complexity). Our bounds on the number of colors turn out to be quite sharp in general. Among other results, we show that no distributed algorithm can color every $n$-vertex planar graph with 4 colors in $o(n)$ rounds.

scholarly journals Equitable list coloring of planar graphs without 4- and 6-cycles

2009 ◽  
Vol 309 (1) ◽  
pp. 280-287 ◽  
Author(s):  
Qiong Li ◽  
Yuehua Bu
Keyword(s):  
Planar Graphs ◽  
List Coloring

scholarly journals Dynamic list coloring of 1-planar graphs

2021 ◽  
Vol 344 (5) ◽  
pp. 112333
Author(s):  
Xin Zhang ◽  
Yan Li
Keyword(s):  
Planar Graphs ◽  
List Coloring
Sign in / Sign up

Export Citation Format

Share Document