关于Gallai路分解猜想的一个结果  

A result on Gallai’s path decomposition

作　　者：初亚男 CHU Yanan(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报(自然科学版)》2025年第1期28-30,73,共4页Journal of Suzhou University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(12201447)。

摘　　要：图G的一个路分解是指将G的边集划分成一些边不交的子集,使得每个子集都是一条路且每条边恰好在一条路上。Gallai猜想每个点数为n的连通图都可分解成[n/2]条路。本文利用Lovász的路-圈构造方法证明当图的偶度点导出子图同构于K_(5),K_(7)或K_(9)时猜想成立。A path decomposition of a graph G is a set of edge-disjoint paths containing all the edges of G.Gallai conjectured that every connected graph on n vertices could be decomposed into[n/2]paths.By applying Lovász’s path-cycle construction,this paper proves that Gallai’s conjecture is true for graphs G in which the subgraph of G induced by all even degree vertices is isomorphic to a K_(5),K_(7) or K_(9).

关 键 词：路 分解 Gallai猜想 

分 类 号：O157.5[理学—数学]