Generalized Turán results for intersecting cliques

Gerbner, Dániel and Patkós, Balázs (2024) Generalized Turán results for intersecting cliques. DISCRETE MATHEMATICS, 347 (1). ISSN 0012-365X

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Abstract

For fixed graphs F and H, the generalized Turán problem asks for the maximum number ex(n, H, F ) of copies of H that an n-vertex F -free graph can have. In this paper, we focus on the case when F is B r,s , the graph consisting of two cliques of size r sharing s common vertices. We determine ex(n, K k , B r,0), ex(n, K k , B r,1) and ex(n, K a,b , B3,1) for all values of a, b, r, k if n is large enough.

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