设Ф是图G的一个正常的顶点染色,若声的任何两种不同颜色所染的顶点数目至多相差1,称声是G的一个均匀染色。对于不含4,5,6-圈的平面图,且最大度△≥9,那么G存在均匀△-染色。
A proper vertex-coloring Ф of a graph G is called an equitable coloring of G if the numbers of vertices in any two-color class differ with each other at most one. Then any planar graph G without 4,5,6-cycles and with △≥19 is equitable 3-colorable.