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- W4309201712 abstract "Given a graph $T$ and a family of graphs $mathcal{F}$, the generalized Tur'an number of $mathcal{F}$ is the maximum number of copies of $T$ in an $mathcal{F}$-free graph on $n$ vertices, denoted by $ex(n,T,mathcal{F})$. When $T = K_r$, $ex(n, K_r, mathcal{F})$ is a function specifying the maximum possible number of $r$-cliques in an $mathcal{F}$-free graph on $n$ vertices. A linear forest is a forest whose connected components are all paths and isolated vertices. Let $mathcal{L}_{k}$ be the family of all linear forests of size $k$ without isolated vertices. In this paper, we obtained the maximum possible number of $r$-cliques in $G$, where $G$ is $mathcal{L}_{k}$-free with minimum degree at least $d$. Furthermore, we give a stability version of the result. As an application of the stability version of the result, we obtain a clique version of the stability of the ErdH{o}s-Gallai Theorem on matchings." @default.
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- W4309201712 date "2022-11-14" @default.
- W4309201712 modified "2023-09-27" @default.
- W4309201712 title "Stability of generalized Tur'an number for linear forests" @default.
- W4309201712 doi "https://doi.org/10.48550/arxiv.2211.07822" @default.
- W4309201712 hasPublicationYear "2022" @default.
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