Generalized Turán problems for complete bipartite graphs

Gerbner, Dániel; Patkós, Balázs

doi:10.48550/arxiv.2101.08094

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2021

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“…Let us show a simpler example where ex na (n, H, F ) = ex(n, H, F ). Gerbner and Patkós [15] showed that if 2 < t < t ′ , then ex(n,…”

Section: Introductionmentioning

confidence: 99%

A non-aligning variant of generalized Turán problems

Gerbner¹

2021

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In the so-called generalized Turán problems we study the largest number of copies of H in an n-vertex F -free graph G. Here we introduce a variant, where F is not forbidden, but we restrict how copies of H and F can be placed in G. More precisely, given an integer n and graphs H and F , what is the largest number of copies of H in an n-vertex graph such that the vertex set of that copy does not contain and is not contained in the vertex set of a copy of F ?We solve this problem for some instances, give bounds in other instances, and we use our results to determine the generalized Turán number for some pairs of graphs.

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“…Let us show a simpler example where ex na (n, H, F ) = ex(n, H, F ). Gerbner and Patkós [15] showed that if 2 < t < t ′ , then ex(n,…”

Section: Introductionmentioning

confidence: 99%