4-正则图中的不连通2-因子  

Disconnected 2-factor of 4-regular graphs

作　　者：胡琳[1] HU Lin(College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830017, China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《内江师范学院学报》2022年第4期43-47,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11961066)。

摘　　要：通过证明顶点个数至少是6的4-正则无爪图中一定包含一个不连通的2-因子,说明了在无爪图中猜想“一个4-正则图是2-因子Hamiltonian的,当且仅当G≌K_(5)”是成立的.因此要继续证明该猜想,只需其对包含K_(1.3)的4-正则图成立即可.By proving that there is a disconnected 2-factor in every 4-regular claw-free graph with at least six vertices,it reveals that conjecture'when and only when G≌K_(5),a 4-regular graph is 2-factor Hamiltonian'is true in claw-free graph.Therefore,to further prove the conjecture,it only needs to guarantee the 4-regular graph containing K_(1.3) to be true.

关 键 词：正则图 2-因子 2-因子Hamiltonian 匹配 

分 类 号：O157.5[理学—数学]