本文選題：點(diǎn)不交　切入點(diǎn)：度條件　出處：《寧夏大學(xué)》2017年碩士論文

【摘要】：圖論是組合數(shù)學(xué)的一個(gè)分支,在各個(gè)領(lǐng)域有著廣泛的應(yīng)用,受到了數(shù)學(xué)界和其他科學(xué)界的重視.本文主要考慮了兩個(gè)問(wèn)題:標(biāo)準(zhǔn)多重二部圖中點(diǎn)不交的4圈的存在性度條件;標(biāo)準(zhǔn)多重圖中點(diǎn)不交的重邊四邊形.本文所指的有向圖為無(wú)環(huán)無(wú)重邊的簡(jiǎn)單有限有向圖.不含環(huán)和重邊的無(wú)向有限圖稱為簡(jiǎn)單圖,頂點(diǎn)集非空且任意兩個(gè)頂點(diǎn)之間的邊數(shù)有限的圖稱為多重圖,任意兩個(gè)頂點(diǎn)之間邊數(shù)至多為2的多重圖稱為標(biāo)準(zhǔn)多重圖.長(zhǎng)為4的圈稱為4圈或者四邊形,圈上的四條邊都為重邊的四邊形稱為重邊四邊形.本文分為四個(gè)部分.第一部分介紹了圖的基本概念以及所研究問(wèn)題的歷史背景和發(fā)展情況.第二部分研究了對(duì)于標(biāo)準(zhǔn)多重二部圖M =(X,Y;E),滿足|X| = |Y| = 2k,k為正整數(shù).如果M中每個(gè)點(diǎn)的度數(shù)至少為3k + 1,則M 一定包含k個(gè)點(diǎn)不交的4圈,使得其中k-1個(gè)為重邊四邊形,剩余一個(gè)四邊形至少有三條重邊.作為推論,我們給出了簡(jiǎn)單二部圖和簡(jiǎn)單有向二部圖中點(diǎn)不交的存在性度條件.第三部分主要研究了對(duì)于階數(shù)為4k,最小度為6k-2的標(biāo)準(zhǔn)多重圖,k為正整數(shù),除三個(gè)特例外,M包含k-1個(gè)重邊四邊形和一個(gè)有三條重邊的四邊形,使得這k個(gè)四邊形彼此點(diǎn)不交.最后提出了一些問(wèn)題,以待進(jìn)一步討論和研究.
[Abstract]:Graph theory is a branch of combinatorial mathematics, which has been widely used in various fields and has been paid attention to by mathematics and other scientific circles. In this paper, two main problems are considered: the existence degree condition of 4 cycles with disjoint points in standard multipartite graphs; The digraph in this paper is a simple finite directed graph with no ring and no multiplicity. An undirected finite graph without ring and reborder is called a simple graph. A graph with a nonempty vertex set and a finite number of edges between two vertices is called a multiplex graph, a multiplex graph with at most 2 edges between any two vertices is called a standard multiplex graph, and a cycle of 4 is called a 4 cycle or a quadrilateral. This paper is divided into four parts. The first part introduces the basic concept of graph and the historical background and development of the problem studied. If X = Y = 2kW k is a positive integer, if the degree of each point in M is at least 3k1, then M must contain 4 cycles with k points disjoint. Such that k-1 is a quadrilateral with a heavy edge, and the remaining quadrilateral has at least three heavy edges. As a corollary, In this paper, we give the existence conditions of disjoint points in simple bipartite graphs and simple directed bipartite graphs. In the third part, we mainly study that the standard multifold graphs with order 4k and minimum degree 6k-2 are positive integers. With the exception of three special exceptions, M contains k-1 double quadrilateral and one quadrilateral with three heavy edges, such that the k quadrilateral does not intersect with each other. Finally, some problems are proposed for further discussion and study.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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相關(guān)期刊論文 前1條

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