【摘要】：圖論的產生和發(fā)展經歷了二百多年的歷史,它是組合數(shù)學的一個重要分支.本文所涉及的圖均指無向簡單有限圖,我們把不含環(huán)和重邊的無向有限圖稱為簡單圖,無爪圖是簡單圖中的一種.如果圖G中不包含與K1,3同構的導出子圖,則稱圖G為無爪圖.K_4~-表示從K4中刪掉任意一條邊所得到的圖.K1,t表示階數(shù)為t + 1的星圖.本文主要討論了有關無爪圖中點不交小階子圖的存在性問題.具體內容如下:(1)介紹了圖論的基本概念和術語以及所研究問題的歷史背景和發(fā)展情況.(2)主要研究了無爪圖中點不交的K1,4.主要結論如下:令k≥ 2且為整數(shù),G是階數(shù)為n,最小度δ(G)≥ 4的無爪圖,如果n ≥ 13k-12,則G至少包含k個點不交的K1,4.(3)主要研究了無爪圖中點不交的K_4~-.主要結論如下:令k≥ 2且為整數(shù),G是階數(shù)為n,最小度δ(G)≥ 5的無爪圖,如果n≥12k-11,則G至少包含k個點不交的K4.(4)在本文的每章末尾,均提出了一個問題,以待進一步討論和研究.
[Abstract]:Graph theory has experienced more than 200 years of history, and it is an important branch of combinatorial mathematics. The graphs in this paper refer to undirected simple finite graphs. We refer to undirected finite graphs without rings and iterated edges as simple graphs, and claw free graphs are one of simple graphs. If a graph G does not contain an derived subgraph which is isomorphic to K1 + 3, then G is called a claw-free graph. K _ s _ 4 denotes a star graph with order t _ 1 that is obtained by deleting any edge from K4. In this paper, we discuss the existence of disjoint subgraphs in claw-free graphs. The main contents are as follows: (1) the basic concepts and terms of graph theory and the historical background and development of the problems studied are introduced. The main results are as follows: let k 鈮，

本文編號：2123259