Acyclic edge coloring of planar graphs with Delta colors
Résumé
An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. In 1978, it was conjectured that ∆( G ) + 2 colors suffice for an acyclic edge coloring of every graph G. The conjecture has been verified for several classes of graphs, however, the best known upper bound for as special class as planar graphs are, is ∆ + 12 (Basavaraju and Chandran, 2009). In this paper, we study simple planar graphs which need only ∆( G ) colors for an acyclic edge coloring. We show that a planar graph with girth g and maximum degree ∆ admits such acyclic edge coloring if g ≥ 12, or g ≥ 8 and ∆ ≥ 4, or g ≥ 7 and ∆ ≥ 5, or g ≥ 6 and ∆ ≥ 6, or g ≥ 5 and ∆ ≥ 10. Our results improve some previously known bounds.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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