An improved bound on acyclic chromatic index of planar graphs

Details An improved bound on acyclic chromatic index of planar graphs An improved bound on acyclic chromatic index of planar graphs

2012-03-23

arxiv.org/abs/1203.5186v1

Mathematics

Combinatorics

Scientific paper

Proper edge coloring of a graph $G$ is called acyclic if there is no bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by $\chi'_a(G)$, is the least number of colors $k$ such that $G$ has an acyclic edge $k$-coloring. Basavaraju et al. [Acyclic edge-coloring of planar graphs, SIAM J. Discrete Math. 25 (2) (2011), 463--478] showed that $\chi'_a(G)\le \Delta(G)+12$ for planar graphs $G$ with maximum degree $\Delta(G)$. In this paper, the bound is improved to $\Delta(G)+10$.

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