不含3-圈和4-圈的平面图的列表均匀染色

Equitable List Coloring of Planar Graphs Without 3 and 4 Cycles

任意给定图G的一个k-一致列表L,若G是L-可染的,且满足每种颜色至多在「|V(G)|/k」个点上出现,则称G是k-均匀可选择的.若图G有一个正常k-顶点染色满足任两个色类中的顶点数至多相差1,则称G是k-均匀可染的.应用discharge方法讨论了不含3-圈和4-圈的平面图的结构,证明了对于不含3-圈和4-圈的平面图G,当k≥{maxΔ(G),6}时,G是k-均匀可选择的,同时G也是k-均匀可染的.

A graph G is equitably k -choosable if for any k -uniform list assignment L,G is L- colorable and each color appears on at most 「｜V（G）/k｜」 vertices. A graph G is equitably k - colorable if G has a proper k - vertex coloring such that the sizes of any two color classes differ by at most 1. We prove in thispaper that every plane graph G without 3 and 4 cycles is equitably k - choosable and equitably k - colorable whenever k≥ max{ （△G） ,6}.