【摘要】：圖論的產(chǎn)生和發(fā)展經(jīng)歷了二百多年的歷史,它是組合數(shù)學(xué)的一個(gè)重要分支.本文把不含環(huán)和重邊的無(wú)向有限圖稱為簡(jiǎn)單圖,無(wú)爪圖是簡(jiǎn)單圖中的一種.如果圖G中不包含同構(gòu)于K1,3的導(dǎo)出子圖,則稱這樣的圖為無(wú)爪圖.K4-表示K4中刪掉任意一條邊所得到的圖.設(shè)G是階數(shù)為n且最小度為δ的無(wú)爪圖,我們給出了G中包含的點(diǎn)不交K4-的個(gè)數(shù)與δ以及n之間的關(guān)系.如果圖的階數(shù)是非空的并且相關(guān)聯(lián)的兩頂點(diǎn)之間的邊數(shù)是有限的,則稱為多重圖,多重圖中每條邊的重?cái)?shù)至多是2且不包含環(huán),則稱之為標(biāo)準(zhǔn)多重圖,記為M.把長(zhǎng)度為4的圈稱為四邊形.定義D是階數(shù)為4k的有向圖且k是非負(fù)整數(shù),設(shè)有向圖D的最小度δ≥6k-2,則D包含k個(gè)點(diǎn)不交有向四邊形,除了圖D同構(gòu)一類特殊圖以外.本文主要考慮了以下幾個(gè)問(wèn)題：無(wú)爪圖中點(diǎn)不交子圖的存在性,多重圖中點(diǎn)不交的四邊形.全文共有四章.第一章介紹了圖的基本概念及所研究問(wèn)題的歷史背景和發(fā)展情況.第二章主要研究了無(wú)爪圖中點(diǎn)不交K4-.主要結(jié)論如下：設(shè)G是階數(shù)為n,最小度δ≥5的無(wú)爪圖,則G至少包含F(xiàn)(n,δ)=(δ-4)(7δ-8)n個(gè)點(diǎn)不交的K4-第三章主要研究了多重圖中點(diǎn)不交的四邊形.主要結(jié)論如下：設(shè)M是頂點(diǎn)數(shù)為4k的標(biāo)準(zhǔn)多重圖,k是非負(fù)的整數(shù),如果δ(M)≥6k-2,那么M包含k個(gè)點(diǎn)不交的Q74,除了M∈{D*,F*}.最后,本文的每章末尾均提出了一個(gè)問(wèn)題,以待進(jìn)一步討論和研究.
[Abstract]:Graph theory has experienced more than 200 years of history, and it is an important branch of combinatorial mathematics. In this paper, an undirected finite graph with no ring and double edges is called a simple graph, and a claw free graph is one of the simple graphs. If a graph G does not contain an derived subgraph which is isomorphic to K1 + 3, then it is called a claw-free graph. K4- denotes the graph obtained by deleting any edge in K4. Let G be a claw free graph of order n and minimum degree 未. We give the relationship between the number of disjoint K4- points contained in G and 未 and n. If the order of a graph is nonempty and the number of edges between two associated vertices is finite, then it is called a multiplex graph. The multiplicity of each edge in a multiplex graph is at most 2 and does not contain a ring. A circle of 4 is called a quadrilateral. It is defined that D is a directed graph of order 4k and k is a non-negative integer, and the minimum degree 未 鈮，

本文編號(hào)：2184764