Planar graphs are 1-relaxed, 4-choosable

Authors:
William Cushing;H. A. Kierstead
Affiliations:
Department of Computer Science, Arizona State University, Tempe, AZ 85287, USA;Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 3
Cited 2

List colourings of planar graphs

Discrete Mathematics
Every planar graph is 5-choosable

Journal of Combinatorial Theory Series B
List Improper Colourings of Planar Graphs

Combinatorics, Probability and Computing

A note on relaxed equitable coloring of graphs

Information Processing Letters
On (3,1 )*-choosability of planar graphs without adjacent short cycles

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that every planar graph G=(V,E) is 1-relaxed, 4-choosable. This means that, for every list assignment L that assigns a set of at least four colors to each vertex, there exists a coloring f such that f(v)@?L(v) for every vertex v@?V and each color class f^-^1(@a) of f induces a subgraph with maximum degree at most 1.