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On generalized Turán problems with bounded matching number
Yisai Xue, Liying Kang · 2024-10-16 · via math.CO updates on arXiv.org

The generalized Turán number $\mathrm{ex}(n, H, \mathcal{F})$ is defined as the maximum number of copies of a graph $H$ in an $n$-vertex graph that does not contain any graph $F \in \mathcal{F}$. 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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