关键词: NIC-平面图, 轻边, 权转移方法, 定向染色

Abstract: If there exists a crossing c in a graph G drawn on the plane, this crossing induces a function [θ:c→][{v1,v2,][v3,v4}], where [{v1,v2,v3,v4}] is a set of four vertices that are the ones incident with the two crossed edges generating the crossing c. If [|θ(c1)∩θ(c2)|≤1] for any two distinct crossings c1 and c2（if exist） in G, G is a NIC-planar graph. It is proven that every NIC-planar graph with girth at least 5 and minimum degree 4 contains an edge with the degrees of the two adjacent vertices both being 4. As a consequence, it deduces that the oriented chromatic number of any NIC-planar graph with girth at least 5 is at most 67.

Key words: NIC-planar graph, light edge, discharging method, oriented coloring