论文标题
最大独立集团和广义壁炉架定理
Maximum Independent Set of Cliques and The Generalized Mantel's Theorem
论文作者
论文摘要
$ k $顶点上任何简单的图形$ g $的完整子图称为$ k $ - \ emph {clique} $ g $。在本文中，我们首先介绍了$ k $ clique（$ k> 1 $）的价值的概念，以扩展给定顶点的程度。然后，我们获得了通用版本的握手引理，我们称之为集团握手引理。 Mantel的众所周知的经典结果指出，带有$ n $ Vertices的三角形图中的最大边数等于$ \ frac {n^{2}}} {4} $。我们的主要目的是使用集团价值和集团握手的引理的想法找到$ k_ {ω+1} $类的上述结果的扩展。
A complete subgraph of any simple graph $G$ on $k$ vertices is called a $k$-\emph{clique} of $G$. In this paper, we first introduce the concept of the value of a $k$-clique ($k>1$) as an extension of the idea of the degree of a given vertex. Then, we obtain the generalized version of handshaking lemma which we call it clique handshaking lemma. The well-known classical result of Mantel states that the maximum number of edges in the class of triangle-free graphs with $n$ vertices is equal to $\frac{n^{2}}{4}$. Our main goal here is to find an extension of the above result for the class of $K_{ω+1}$-free graphs, using the ideas of the value of cliques and the clique handshaking lemma.
