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The smallest degree sum that yields potentially $C_k$ -graphical sequences

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摘要: Summary: "In this paper we consider a variation of the classical Turán-type extremal problems. Let $S$be an $n$-term graphical sequence, and $\sigma(S)$be the sum of the terms in $S$. Let $H$be a graph. The problem is to determine the smallest even $l$such that any $n$-term graphical sequence $S$having $\sigma(S)\geq l$has a realization containing $H$as a subgraph. Denote this value $l$by $\sigma(H,n)$. We show $\sigma(C_{2m+1},n)=m(2n-m-1)+2$, for $m\geq 3$, $n\geq 3m$; $\sigma(C_{2m+2},n)=m(2n-m-1)+4$, for $m\geq 3$, $n\geq 5m-2$.''
 

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[V2] 2024-02-18 12:20:52 ChinaXiv:202402.00154V2 下载全文
[V1] 2024-02-10 10:42:40 ChinaXiv:202402.00154v1 查看此版本 下载全文
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