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
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
Random Structures & Algorithms
Note: Improved bounds for acyclic chromatic index of planar graphs
Discrete Applied Mathematics
Acyclic chromatic indices of planar graphs with large girth
Discrete Applied Mathematics
Acyclic chromatic indices of fully subdivided graphs
Information Processing Letters
The acyclic edge coloring of planar graphs without a 3-cycle adjacent to a 4-cycle
Discrete Applied Mathematics
Acyclic edge coloring of graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let G=(V,E) be any finite graph. A mapping c:E-[k] is called an acyclic edgek-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, denoted by @g^'(G). In 1978, Fiamcik conjectured that for any graph G it holds @g^'(G)@?@D(G)+2, where @D(G) stands for the maximum degree of G. This conjecture has been verified by now only for some special classes of graphs. In 2010, Borowiecki and Fiedorowicz confirmed it for planar graph with girth at least 5. In this paper, we improve the above result, by proving that if G is a plane graph such that for each pair i,j@?{3,4}, no i-face and a j-face share a common vertex in G, then @g^'(G)@?@D(G)+2.