C60的完美匹配与Hamilton圈
Perfect Matchings and Hamiltonian Cycles of C60
DOI: 10.12677/PM.2020.108088, PDF,    国家自然科学基金支持
作者: 马聪聪, 王倩倩, 姚海元*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 完美匹配；C60；Hamilton圈；Perfect Matchings； C60； Hamiltonian Cycles
摘要: 设G是一个3-正则的连通图。删掉G一个Hamilton圈(删边不删点)后剩下的子图是G的一个完美匹配；反之，删掉G一个完美匹配后剩下的子图只要是连通的，那一定是原图的Hamilton圈。因此本文通过删除完美匹配的方法给出了Buckminsterfullerene (C60)的所有Hamilton圈，进而通过Hamilton圈研究了完美匹配之间的关系。
Abstract: Let G be a 3-regular connected graph. If we delete a Hamiltonian cycle of G (delete edges but not vertices), then the rest graph is a perfect matching of G. On the contrary, the rest subgraph deleting a perfect matching of G must be Hamiltonian cycle of G provided that it is connected. Consequently, all Hamiltonian cycles of C60 are given in this paper by the way of deleting perfect matchings. And then it is shown that the relationship of perfect matchings is obtained by Hamiltonian cycles.
文章引用：马聪聪, 王倩倩, 姚海元. C60的完美匹配与Hamilton圈[J]. 理论数学, 2020, 10(8): 745-763. https://doi.org/10.12677/PM.2020.108088

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