On generalized Turán problems with bounded matching number

2024/10/16 by Xue, Yisai, Kang, Liying
#05C35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.12338

Abstract

The generalized Turán number ex(n, H, F) is defined as the maximum number of copies of a graph H in an n-vertex graph that does not contain any graph F ∈ F. Alon and Frankl initiated the study of Turán problems with a bounded matching number.In this paper, we establish stability results for generalized Turán problems with bounded matching number.Using the stability results, we provide exact values of \ex(n,K_r,\F,M_s+1\) for F being any non-bipartite graph or a path on k vertices.

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