没有7-圈的平面图的BB-染色❋

摘要

研究了没有7-圈的连通平面图的BB-染色问题。应用经典的Discharging方法,证明了没有7-圈且不含相邻4-圈的连通平面图G,存在G的一棵生成树T,使得( G,T)是BB-4-可染的。这一结果进一步拓展了平面图的BB-4-可染的充分条件。%The problem of backbone coloring of connected planar graphs without 7-cycles was studied. By using the discharging technique, it was proved that if G is a connected planar graph without 7-cycles and adjacent 4-cycles, then there would have a spanning tree T of G such that ( G,T) is BB-4-colorable. The result generalized the sufficient condition for the planar graphs of BB-4-colorable.