Extremal graphs for intersecting cliques

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Abstract

For any two positive integers nr⩾1, the well-known Turán Theorem states that there exists a least positive integer ex(n,Kr) such that every graph with n vertices and ex(n,Kr)+1 edges contains a subgraph isomorphic to Kr. We determine the minimum number of edges sufficient for the existence of k cliques with r vertices each intersecting in exactly one common vertex.

MSC

05C78

Keywords

Extremal graph
Turán graph
Cliques
Matchings

Cited by (0)

1

Supported by NSF Grant DMS-0070059.

2

Supported by NNSF of China and the innovation funds of Institute of Systems Science, AMSS, CAS.