符号图的模流

发布时间：2018-01-14 05:11

本文关键词：符号图的模流　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：为攻克四色猜想,Tutte在1954年提出了整数流理论.此后,整数流理论成为图论一个重要的研究分支.上世纪五十年代,Tutte证明了普通图存在处处非零的k-流当且仅当它存在处处非零的模k-流.然而,这种等价关系在符号图上并不成立.因此,研究者期望通过研究符号图的模流,揭示符号模流与符号整数流之间的关系,从而达到研究符号整数流的目的.本文主要讨论了符号图上模流的几个问题,给出了符号图上的模流多项式及其基本性质,确定了一类图的最小模流值,证明了每一个有模流的符号图存在处处非零的模6-流,并给出了Bouchet符号6-流猜想的一个等价命题.本文的组织结构如下:第一章首先介绍了符号流理论的研究背景,常用的概念和术语,再介绍了本文的研究问题,研究进展及主要结果.第二章首先介绍了符号图上流的基本性质,以及一个重要的概念转换操作等价及其性质.其次,我们定义了符号图模流多项式,并讨论了其基本性质.最后,确定了一类特殊图的最小模流值.第三章给出了符号图存在处处非零模流的三个等价命题,再证明了每一个有模流的符号图存在处处非零的模6-流,最后给出Bouchet符号6-流猜想的一个等价命题.
[Abstract]:In 1954, Tutte put forward the integer flow theory in order to conquer the four-color conjecture. Since then, integer flow theory has become an important research branch of graph theory. -50s. Tutte proved that a normal graph has a everywhere non-zero k-flow if and only if it exists a everywhere non-zero modular k-stream. However, this equivalence relation does not hold on the symbolic graph. The researcher expects to reveal the relationship between symbol mode flow and symbol integer flow by studying the mode flow of symbol graph, so as to achieve the purpose of studying symbol integer flow. This paper mainly discusses several problems of symbol mode flow on symbol graph. In this paper, the modular flow polynomials on signed graphs and their basic properties are given, the minimum mode flow values of a class of graphs are determined, and it is proved that there exists everywhere non-zero modular 6-flow in every signed graph of a modular flow. An equivalent proposition of Bouchet symbolic 6-flow conjecture is given. The organizational structure of this paper is as follows: the first chapter introduces the background of symbolic flow theory, the commonly used concepts and terms. In the second chapter, we introduce the basic properties of the flow on the symbolic graph, an important conceptual transformation operation equivalence and its properties. We define the modular flow polynomials of symbolic graphs and discuss their basic properties. Finally, we determine the minimum mode flow values of a class of special graphs. In chapter 3, we give three equivalent propositions that there exists everywhere non-zero mode flows in signed graphs. It is also proved that every sign graph of a module-flow has a non-zero modulus 6-stream everywhere. Finally, an equivalent proposition of Bouchet symbolic 6-flow conjecture is given.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

【相似文献】