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arXiv · 2503.07386

On generalized Tur{á}n problems with bounded matching number and circumference

Yongchun Lu·Liying Kang·Yisai Xue
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Abstract

Let \( \mathcal{F} \) be a family of graphs. The generalized Turán number \( \operatorname{ex}(n, K_r, \mathcal{F}) \) is the maximum number of $K_r$ in an \( n \)-vertex graph that does not contain any member of \( \mathcal{F} \) as a subgraph. Recently, Alon and Frankl initiated the study of Turán problems with bounded matching number. In this paper, we determine the generalized Turán number of \( C_{\geq k} \) with bounded matching number.

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Yongchun Lu, Liying Kang, Yisai Xue. 2025-03-17. On generalized Tur{á}n problems with bounded matching number and circumference. https://arxiv.org/abs/2503.07386

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