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On generalized Tur\'an problems with bounded matching number

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arxiv 2410.12338 v1 pith:QASDNPGQ submitted 2024-10-16 math.CO

classification math.CO
keywords numbergraphboundedgeneralizedmatchingproblemsmathcalresults
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abstract

The generalized Tur\'an 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 Tur\'an problems with a bounded matching number.In this paper, we establish stability results for generalized Tur\'an 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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spectral extremal problems for degenerate graphs

    math.CO 2025-07 conditional novelty 7.0 of 10

    For finite degenerate graph families with linear ex(n,F), the spectral extremal graph is characterized by the independent covering number β'(F) and the induced family H(F).

  2. Tur\'an numbers of cycles plus a general graph

    math.CO 2024-11 conditional novelty 6.0 of 10

    The Turan number ex(n,{C>=k,F}) is determined up to an additive constant for every 2-connected F with p(F) at least floor((k-1)/2)+1; the even-k formula is n times the larger of (k-2)/2 and ex(k-1,F)/(k-2), plus O_k(1).

  3. Survey of generalized Tur\'an problems -- counting subgraphs

    math.CO 2025-06 conditional novelty 2.0 of 10

    A survey of what is known about maximizing the count of one fixed subgraph in graphs that avoid another fixed subgraph.

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