Generalized Turán Problems for Small Graphs

Gerbner, Dániel (2023) Generalized Turán Problems for Small Graphs. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 43 (2). pp. 549-572. ISSN 1234-3099

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Abstract

For graphs H and F , the generalized Turán number ex(n, H, F ) is the largest number of copies of H in an F -free graph on n vertices. We consider this problem when both H and F have at most four vertices. We give sharp results in almost all cases, and connect the remaining cases to well-known unsolved problems. Our main new contribution is applying the progressive induction method of Simonovits for generalized Turán problems.

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