多重图的处处无零整数流  

Nowhere-Zero Integer Flows in the Multigraphs

作　　者：张真 张军阳 ZHANG Zhen;ZHANG Junyang(College 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4期32-35,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11671276);重庆师范大学人才引进/博士启动项目(No.21XLB006);重庆市基础研究与前沿探索项目(No.cstc2018jcyjAX0010)。

摘　　要：【目的】探讨多重图与它的基图的处处无零整数流的存在性之间的关系。【方法】用原图的处处无零整数流构造新图的处处无零整数流。【结果】1)若一个多重图的基图存在处处无零k-流,则它也存在处处无零k-流;2)如果两个多重图有共同的基图,并且它们的任意一条公共边都是基图中某个边的平行边,那么这两个多重图的处处无零k-流的存在性一致。【结论】得到的结果不但有助于对处处无零整数流这一概念的理解,还可应用到简单图的处处无零整数流的研究中。[Purposes]Investigate the relationship between the existence of nowhere-zero integer flows of a multigraph and its base graph.[Methods]Use nowhere-zero integer flows of original graphs to construct nowhere-zero integer flows of new graphs.[Findings]There are two main results:1)If the base graph of a multigraph has a nowhere-zero k-flow,then it also has a nowhere-zero k-flow.2)If two multigraphs have a common base graph and each of their common edges is a parallel edge of an edge in the base graph,then the existence of nowhere-zero k-flows of the two multigraphs is identical.[Conclusions]The main results are not only helpful to understand the concept of nowhere-zero integer flow,but also can be applied to the study of nowhere-zero integer flows of simple graphs.

关 键 词：多重图 整数流 处处无零整数流 

分 类 号：O186.1[理学—数学]