无爪图上点不交小阶子图的存在性研究

发布时间：2018-07-15 07:16

【摘要】：图论的产生和发展经历了二百多年的历史,它是组合数学的一个重要分支.本文所涉及的图均指无向简单有限图,我们把不含环和重边的无向有限图称为简单图,无爪图是简单图中的一种.如果图G中不包含与K1,3同构的导出子图,则称图G为无爪图.K_4~-表示从K4中删掉任意一条边所得到的图.K1,t表示阶数为t + 1的星图.本文主要讨论了有关无爪图中点不交小阶子图的存在性问题.具体内容如下:(1)介绍了图论的基本概念和术语以及所研究问题的历史背景和发展情况.(2)主要研究了无爪图中点不交的K1,4.主要结论如下:令k≥ 2且为整数,G是阶数为n,最小度δ(G)≥ 4的无爪图,如果n ≥ 13k-12,则G至少包含k个点不交的K1,4.(3)主要研究了无爪图中点不交的K_4~-.主要结论如下:令k≥ 2且为整数,G是阶数为n,最小度δ(G)≥ 5的无爪图,如果n≥12k-11,则G至少包含k个点不交的K4.(4)在本文的每章末尾,均提出了一个问题,以待进一步讨论和研究.
[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，

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