广义Petersen图的2-HC-可扩性  

2-HC-extendability of generalized Petersen graphs

作　　者：王锦伟 WANG Jinwei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2024年第6期712-717,共6页Journal of Zhejiang University（Science Edition）

基　　金：兰州交通大学校青年基金项目(2022027).

摘　　要：结合连通图的可扩性和哈密尔顿性,2012年MIKLAVIC等提出了连通图的可扩性。如果连通图Γ包含l-路且每条l-路均可扩充为Γ的一条哈密尔顿圈,那么称Γ是l-HC-可扩的。利用连通图的圈的对称差构造哈密尔顿圈,并证明了广义Petersen图GP(n,k)是2-HC-可扩的,其中k=1,2和3。In 2012,MIKLAVIC et al gave the definition of the l-HC-extendability by combining the extendability of connected graphs with hamiltonicity.Based on their study,a connected graphΓis l-HC-extendable if it contains a path of length l and every such path could be extended to a Hamilton cycle inΓ.In this paper,inspired by their study,we aim to study the l-HC-extendability of the generalized Petersen graphs GP(n,k).We prove that the generalized Petersen graphs GP(n,k)is 2-HC-extendable,where k=1,2,3.

关 键 词：广义PETERSEN图 l-路 自同构 哈密尔顿圈 HC-可扩性 

分 类 号：O157.5[理学—数学]