张孝伍^*

（  青岛理工大学理学院，青岛 266520；  ）

摘要： 给出了平面三次图的递归构造方法，同时给出极大平面图的构造方法，构造出所有极大平面图，证明了任何极大平面图是四着色的。
关键词： 极大平面图；平面三次图；对偶平面图；节点着色；着二色子图

ZHANG Xiaowu^*

（  College of Science, Qingdao University of Technology, Qingdao 266520；  ）

Abstract： The structural method of maximal planar graph was given, and a new proof for four-colour theorem was got. In this paper, we had gotted the recursive structural method of plane cubic graph and the structural method of maximal planar graph, we can constructed all maximal planar graphs. We proofed that the arbitrary maximal planar graphs are four colorable.

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