次立方平面图的单射边染色

如果3条边e₁,e₂,e₃按照此顺序形成一条长为3的路或者圈,则称这3条边是连续的.k-单射边染色是对图G的边进行染色,使得如果3条边e₁,e₂,e₃是连续的,那么,e₁和e₃染不同的颜色.图G的单射边色数为所有单射边染色中所用颜色最少的颜色数.文中考虑在限制围长条件下,次立方平面图G的单射边色数.

Injective Edge Coloring of Planar Subcubic Graphs

If three edges e₁, e₂, e₃ form a path or cycle of length three in this order, they are called consecutive. A k-injective edge coloring is a coloring of the edges of G, such that if e₁, e₂, e₃ are consecutive, then e₁ and e₃ receive distinct colors. The injective edge coloring number is the smallest number of colors used in all injective edge colorings of G. In this paper, we consider the injective edge coloring numbers of the planar subcubic graphs in terms of the girth of G.