Further result on acyclic chromatic index of planar graphs
نویسندگان
چکیده
An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). In this paper, we prove that every planar graph G admits an acyclic edge coloring with ∆(G) + 6 colors.
منابع مشابه
An improved bound on acyclic chromatic index of planar graphs
A 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 χ′a(G), is the least number of colors k such that G has an acyclic edge k-coloring. Basavaraju et al. [Acyclic edgecoloring of planar graphs, SIAM J. Discrete Math. 25 (2) (2011), 463–478] showed that χ′a(G) ≤ ∆(G) + 12 for planar graphs G with maximum degree...
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 201 شماره
صفحات -
تاریخ انتشار 2016