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On generalized Tur\'an problems with bounded matching number
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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.
Forward citations
Cited by 3 Pith papers
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Tur\'an numbers of cycles plus a general graph
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).
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Survey of generalized Tur\'an problems -- counting subgraphs
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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