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- W4366999729 abstract "Given a graph $T$ and a family of graphs $mathcal{H}$. The generalized Tur'an number of $mathcal{H}$ is the maximum number of copies of $T$ in an $mathcal{H}$-free graph on $n$ vertices, denoted by $ex(n, T, mathcal{H})$. Let $ex(n, T, mathcal{H})$ denote the maximum number of copies of $T$ in an $n$-vertex $mathcal{H}$-free graph. Recently, Alon and Frankl (arXiv2210.15076) determined the exact values of $rm{ex}(n, {K_{r+1}, M_{s+1}})$, where $K_{r+1}$ and $M_{s+1}$ are complete graph on $r + 1$ vertices and matching of size $s + 1$, respectively. Ma and Hou (arXiv2301.05625) gave the generalized version of Alon and Frankl's Theorem, which determine the exact values of $ex(n, K_r, {K_{k+1}, M_{s+1}})$. Zhang determined the exact values of $ex(n, K_r, mathcal{L}_{n, s})$, where $mathcal{L}_{n, s}$ be the family of all linear forests of order $n$ with $s$ edges. Inspired by the work of Zhang and Ma, in this paper, we determined the exact number of $ex(n, {K_{r+1}, mathcal{L}_{n, s}})$." @default.
- W4366999729 created "2023-04-27" @default.
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- W4366999729 date "2023-04-23" @default.
- W4366999729 modified "2023-10-18" @default.
- W4366999729 title "Tur'an problems for linear forests and cliques" @default.
- W4366999729 doi "https://doi.org/10.48550/arxiv.2304.11645" @default.
- W4366999729 hasPublicationYear "2023" @default.
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