Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Acyclic colorings of subcubic graphs
Information Processing Letters
Analysis of a heuristic for acyclic edge colouring
Information Processing Letters
Acyclic edge colorings of graphs
Journal of Graph Theory
Acyclic Edge Colouring of Outerplanar Graphs
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
About acyclic edge colourings of planar graphs
Information Processing Letters
Acyclic edge coloring of graphs with maximum degree 4
Journal of Graph Theory
Note: Acyclic edge coloring of planar graphs with large girth
Theoretical Computer Science
Acyclic edge chromatic number of outerplanar graphs
Journal of Graph Theory
Some results on acyclic edge coloring of plane graphs
Information Processing Letters
Information Processing Letters
Random Structures & Algorithms
Acyclic edge colouring of plane graphs
Discrete Applied Mathematics
Acyclic edge coloring of graphs
Discrete Applied Mathematics
| Hi-index | 0.89 |
Let G=(V,E) be any finite simple graph. A mapping @f:E-[k] is called an acyclic edge k-colouring of G, if any two adjacent edges have different colours and there are no bichromatic cycles in G. The smallest number k of colours such that G has an acyclic edge k-colouring is called the acyclic chromatic index of G and is denoted by @g"a^'(G). Fiamcik proved that @D(G)@?(@D(G)-1)+1 is an upper bound for the acyclic chromatic index of a graph G and conjectured that @g"a^'(G)==3 or G is acyclic. Our proof is constructive and hence yields a polynomial time algorithm. This result is an extension of a result obtained in 1984 by Fiamcik for subdivisions of cubic graphs and improves a recent result presented by Muthu et al.