2-连通无爪图中的2-因子  

2-factors in 2-connected claw-free graphs

作　　者：王雅云 雷万鹏 WANG Ya-yun;LEI Wan-peng(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《青海师范大学学报(自然科学版)》2024年第4期62-66,106,共6页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：山西省基础研究计划(自由探索类)面上项目(20210302124303)。

摘　　要：为了解决无爪图中2-因子的存在性问题,提出了一个在独立数条件下的2-连通无爪图中2-因子的充分条件,由于2-因子的存在性问题和哈密尔顿问题一样都是NP完全问题,故运用Ryjácek提出的2-因子加强闭包作为工具,将无爪图中2-因子转化为某一个线图原图的d-系统.利用反证法,通过闭包转化后线图原图围长和周长的特征,分情况讨论并分析其拓扑结构,进而完全刻画在独立数条件下的2-连通无爪图的2-因子,进一步揭示了无爪图在独立数条件下的拓扑结构,为今后2-因子的研究提供了新的思想和方法.To solve the existence problem of 2-factors in claw-free graphs,a sufficient condition for 2-factors in 2-connected claw-free graphs under the condition of independence number is proposed.Since the existence problem of 2-factors,like the Hamiltonian problem,is an NP-complete problem,the 2-factor strengthened closure proposed by Ryjácek is used as a tool to transform the 2-factor in claw-free graphs into d-system of the original graph of a certain line graph.By using the reductio ad absurdum method,through the characteristics of the girth and circumference of the original graph of the line graph after the closure transformation,the topological structure is discussed and analyzed in different cases,thereby completely characterizing the 2-factor of 2-connected claw-free graphs under the condition of independence number.This further reveals the topological structure of claw-free graphs under the condition of independence number and provides new ideas and methods for the future research of 2-factors.

关 键 词：闭包 d-系统 无爪图 本质2-边连通 

分 类 号：O157.6[理学—数学]