A Sufficient Condition for Planar Graph to be Class One
Xiaodong Li · Bulletin of Science and Technology · 2012
The graph is of Class one if chromatic index is the maximum degree.It is proved that if G is a planar graph with maximum degree 6,and for each vertex v,there is an integer kv∈{3,4,5} such that vkv-C,then G is class one,where vkv-C denotes that v does not on a kv-cycle of G.