On clique values identities and mantel-type theorems
Publish place: Transactions on Combinatorics، Vol: 9، Issue: 3
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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JR_COMB-9-3_002
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
In this paper, we first extend the weighted handshaking lemma, using a generalization of the concept of the degree of vertices to the values of graphs. This edge-version of the weighted handshaking lemma yields an immediate generalization of the Mantel's classical result which asks for the maximum number of edges in triangle-free graphs to the class of $K_{۴}$-free graphs. Then, by defining the concept of value for cliques (complete subgraphs) of higher orders, we also extend the classical result of Mantel for any graph $G$. We finally conclude our paper with a discussion about the possible future works.
Authors
Hossein Faal
Department of Mathematics and Computer Science, Allameh Tabatabai University, Tehran, Iran.