An edge-coloring of a graph G is an coloring of a graph G is an edge-coloring of G such assignment of colors to all the edges of G. A go- that each color appears at each vertex at least g（v） times. The maximum integ...An edge-coloring of a graph G is an coloring of a graph G is an edge-coloring of G such assignment of colors to all the edges of G. A go- that each color appears at each vertex at least g（v） times. The maximum integer k such that G has a go-coloring with k colors is called the gc-chromatic index of G and denoted by X＇gc （G）. In this paper, we extend a result on edge-covering coloring of Zhang X＇gc（ ） = δg（G）, and Liu in 2011, and give a new sufficient condition for a simple graph G to satisfy ＇ x＇gc（G）=δg（G）,where δg（G）=minv∈V（G）{[d（v）/g（v）]}.展开更多
基金Supported by Shandong Provincial Natural Science Foundation,China(Grant No.ZR2014JL001)the Shandong Province Higher Educational Science and Technology Program(Grant No.J13LI04)the Excellent Young Scholars Research Fund of Shandong Normal University of China
文摘An edge-coloring of a graph G is an coloring of a graph G is an edge-coloring of G such assignment of colors to all the edges of G. A go- that each color appears at each vertex at least g（v） times. The maximum integer k such that G has a go-coloring with k colors is called the gc-chromatic index of G and denoted by X＇gc （G）. In this paper, we extend a result on edge-covering coloring of Zhang X＇gc（ ） = δg（G）, and Liu in 2011, and give a new sufficient condition for a simple graph G to satisfy ＇ x＇gc（G）=δg（G）,where δg（G）=minv∈V（G）{[d（v）/g（v）]}.
