For any two positive integers n greater than or equal to r greater than or equal to 1, the well-known Turan Theorem states that there exists a least positive integer ex(n, K-r) such that every graph with n vertices and ex(n, K-r) + 1 edges contains a subgraph isomorphic to K-r. We determine the minimum number of edges sufficient for the existence of k cliques with r vertices each intersecting in exactly one common vertex. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 4]
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