Optimal acyclic edge-coloring of cubic graphs

Authors:
Lars Døvling Andersen;Edita Máčajová;Ján Mazák
Affiliations:
Department of Mathematical Sciences, Aalborg University, 9220, Aalborg SØ, Denmark;Department of Computer Science, Faculty of Mathematics, Physics and Informatics Comenius University, 842 48, Bratislava, Slovakia;Department of Computer Science, Faculty of Mathematics, Physics and Informatics Comenius University, 842 48, Bratislava, Slovakia
Venue:
Journal of Graph Theory
Year:
2012

Citing 5
Cited 2

Further algorithmic aspects of the local lemma

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Acyclic edge colorings of graphs

Journal of Graph Theory
The acyclic edge chromatic number of a random d-regular graph is d + 1

Journal of Graph Theory
Acyclic edge coloring of graphs with maximum degree 4

Journal of Graph Theory
Acyclic coloring of graphs

Random Structures & Algorithms

Acyclic edge coloring of planar graphs with girth at least 5

Discrete Applied Mathematics
Acyclic edge coloring of graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

An acyclic edge-coloring of a graph is a proper edge-coloring such that the subgraph induced by the edges of any two colors is acyclic. The acyclic chromatic index of a graph G is the smallest number of colors in an acyclic edge-coloring of G. We prove that the acyclic chromatic index of a connected cubic graph G is 4, unless G is K4 or K3,3; the acyclic chromatic index of K4 and K3,3 is 5. This result has previously been published by Fiamčík, but his published proof was erroneous. © 2012 Wiley Periodicals, Inc.