本文關(guān)鍵詞：符號圖的模流　出處：《安徽大學》2017年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 模流 符號圖 流多項式 6-流猜想

【摘要】：為攻克四色猜想,Tutte在1954年提出了整數(shù)流理論.此后,整數(shù)流理論成為圖論一個重要的研究分支.上世紀五十年代,Tutte證明了普通圖存在處處非零的k-流當且僅當它存在處處非零的模k-流.然而,這種等價關(guān)系在符號圖上并不成立.因此,研究者期望通過研究符號圖的模流,揭示符號模流與符號整數(shù)流之間的關(guān)系,從而達到研究符號整數(shù)流的目的.本文主要討論了符號圖上模流的幾個問題,給出了符號圖上的模流多項式及其基本性質(zhì),確定了一類圖的最小模流值,證明了每一個有模流的符號圖存在處處非零的模6-流,并給出了Bouchet符號6-流猜想的一個等價命題.本文的組織結(jié)構(gòu)如下:第一章首先介紹了符號流理論的研究背景,常用的概念和術(shù)語,再介紹了本文的研究問題,研究進展及主要結(jié)果.第二章首先介紹了符號圖上流的基本性質(zhì),以及一個重要的概念轉(zhuǎn)換操作等價及其性質(zhì).其次,我們定義了符號圖模流多項式,并討論了其基本性質(zhì).最后,確定了一類特殊圖的最小模流值.第三章給出了符號圖存在處處非零模流的三個等價命題,再證明了每一個有模流的符號圖存在處處非零的模6-流,最后給出Bouchet符號6-流猜想的一個等價命題.
[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.
【學位授予單位】：安徽大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O157.5

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1 包磊;符號圖的模流[D];安徽大學;2017年

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本文編號：1422142