平图的四着色与对偶图的H圈  

Hamiltonian Cycle in Planar Graph and 4-colouring of the Dual

作　　者：侴万禧[1] 霍玉洪[1] 李晓毅[2] 

机构地区：[1]安徽理工大学土木建筑学院,安徽淮南232001 [2]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2009年第3期264-266,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10471096)

摘　　要：阐明了平图中的H圈与对偶图顶点四着色的依存关系。提出了平图的顶点四着色和对偶图顶点四着色的具体步骤。介绍了多面体平图的H圈分解与对偶图顶点四着色,以及对偶图的H圈分解与平图的顶点四着色。讨论了平图及对偶图的H圈的个数,森林Fi的个数及顶点四着色方案数。The interdependent relationship between the Hamiltonian cycle and 4-colouring of the planar graph in the dual have discussed. The step for 4-colouring the planar graph and the dual of planar has given. The decomposition into Hamiltonian cycle and 4-colouring of the planar graph in ＂the dual; and ＂the decomposition into Hamiltonian cycle in the dual and 4-colouring of the planar graph are proposed. The number of planar graph and the dual graph, of the forest Fi, and of the 4-colouring planning are discussed.

关 键 词：H圈 平图 对偶图 四着色 

分 类 号：O157[理学—数学]