短圈覆盖与处处无零4-流  

Short Circle Coverage and Nowhere-Zero 4-Flow

作　　者：路娜 张军阳 LU Na;ZHANG Junyang(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第1期137-140,共4页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市基础研究与前沿探索项目(No.cstc2018jcyiAX0010);重庆师范大学人才引进/博士启动项目(No.21XLB006)。

摘　　要：【目的】针对一些特殊的图类验证Tutte的4-流猜想。【方法】用子图的处处无零4-流构造原图的处处无零4-流。【结果】1)若图G=n∪i=1Gi,其中G;存在处处无零4-流,1≤i≤n,且l-1∪i=1与G;最多有两条公共边,2≤l≤n,则G存在处处无零4-流;2)若图G=H∪F,其中H是G的一个存在处处无零4-流的子图,F是G的一个阶数不超过4的无桥连通子图,则G存在处处无零4-流;3)若图G的每条边都包含在一个长度不超过4的圈中,则G存在处处无零4-流。【结论】上述的第2个结果是Catlin的一个引理的推广;Imrich和?krekovski关于笛卡尔积图的处处无零4-流的结果是上述第3个结果的一个直接推论。[Purposes]Verify Tutte’s 4-flow conjecture for some special classes of graphs.[Methods]Use the nowhere-zero 4-flow of subgraphs to construct the nowhere-zero 4-flow of original graphs.G=n∪i=1Gi graph where every G;is a subgraph of G admitting a nowhere-zero 4-flow.If there are at most two common edges betweenl-1∪i=1for each 2≤l≤n,then Gadmits a nowhere-zero 4-flow.2)If a graph G=H∪F where H admits a nowhere-zero 4-flow and F is a bridgeless graph of order at least 4,then G admits a nowhere-zero 4-flow.3)If each edge of a graph Gis contained in cycle of length at most 4,then G admits a nowhere-zero 4-flow.[Conclusions]Our second result is a generalization of Catlin’s lemma.The result on the existence of nowhere-zero 4-flows of Cartesian product graphs given by Imrich and?krekovsk is a direct corollary of our third result.

关 键 词：整数流 处处无零4-流 笛卡尔积图 

分 类 号：O186.1[理学—数学]