5-正则图的路分解  

Path decompositions of 5-regular graphs

作　　者：初亚男 范更华[2] 洪明珠 周垂香[2] Yanan Chu;Genghua Fan;Mingzhu Hong;Chuixiang Zhou

机构地区：[1]苏州科技大学数学科学学院,苏州215009 [2]福州大学离散数学研究中心,福州350108

出　　处：《中国科学：数学》2024年第11期1787-1794,共8页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12201447,11971110和12271099)资助项目。

摘　　要：对于正则图的路分解问题,Favaron等(2010)提出猜想:对于奇数l,任意包含一个完美匹配的l-正则图可以分解成长度为l的路.当l=5时,Favaron等(2010)证明了不含4-圈时猜想成立.后来Botler等(2015)证明了不含3-圈时猜想成立.本文证明当l=5且图中任意3-圈与4-圈的交为空集时,猜想成立.Let l be an odd integer.It was conjectured that every l-regular graph containing a perfect matching can be decomposed into paths of length l.For the case l=5,Favaron et al.(2010)veri ed the conjecture for graphs with no cycle of length 4,and Botler et al.(2015)veri ed it for triangle-free graphs.In this paper,we prove that every 5-regular graph with a perfect matching can be decomposed into paths of length 5,provided that 3-cycles and 4-cycles in the graph have no edge in common.

关 键 词：分解 路 正则图 

分 类 号：O157.5[理学—数学]