Acyclic chromatic indices of planar graphs with large girth
An acyclic edge coloring of a graph G G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a?(G) a ? ( G ) of G G is the smallest k k such that G G has an acyclic edge coloring using k k colors. In this paper, we prove that every planar graph G G with girth g(G) g ( G ) and maximum degree ? ? has a?(G)=? a ? ( G ) = ? if there exists a pair (k,m)?{(3,11),(4,8),(5,7),(8,6)} ( k , m ) ? { ( 3 , 11 ) , ( 4 , 8 ) , ( 5 , 7 ) , ( 8 , 6 ) } such that G G satisfies ??k ? ? k and g(G)?m g ( G ) ? m .
planar graph girth acyclic edge coloring acyclic chromatic index