Acyclic and oriented chromatic numbers of graphs
Journal of Graph Theory
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
The acyclic edge chromatic number of a random d-regular graph is d + 1
Journal of Graph Theory
Optimal acyclic edge colouring of grid like graphs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Some results on acyclic edge coloring of plane graphs
Information Processing Letters
Information Processing Letters
Note: Improved bounds for acyclic chromatic index of planar graphs
Discrete Applied Mathematics
On acyclic edge coloring of toroidal graphs
Information Processing Letters
Acyclic chromatic indices of planar graphs with large girth
Discrete Applied Mathematics
Improved bounds on coloring of graphs
European Journal of Combinatorics
Acyclic edge coloring of planar graphs without 5-cycles
Discrete Applied Mathematics
Acyclic edge colouring of plane graphs
Discrete Applied Mathematics
Acyclic chromatic indices of fully subdivided graphs
Information Processing Letters
A new upper bound on the acyclic chromatic indices of planar graphs
European Journal of Combinatorics
Acyclic edge coloring of graphs
Discrete Applied Mathematics
| Hi-index | 0.00 |
An acyclicedge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest. The acyclic chromatic indexof a graph is the minimum number ksuch that there is an acyclic edge colouring using kcolours and is usually denoted by a茂戮驴(G). Determining a茂戮驴(G) exactly is a very hard problem (both theoretically and algorithmically) and is not determined even for complete graphs. We show that a茂戮驴(G) ≤ Δ(G) + 1, if Gis an outerplanar graph. This bound is tight within an additive factor of 1 from optimality. Our proof is constructive leading to an $O\!\left({n \log \Delta}\right)$ time algorithm. Here, Δ= Δ(G) denotes the maximum degree of the input graph.