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

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:2402.06001

J. Combin. Math. Combin. Comput. , 49, 57–64. , 2004.5
"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 $m\geq 3$ , $n\geq 5m-2$ .''
graphical sequence; cycle
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@inproceedings{lai2004the,
  title={The smallest degree sum that yields potentially $C_k$ -graphical sequences},
  author={Lai Chunhui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240210105218779870764},
  booktitle={J. Combin. Math. Combin. Comput. },
  volume={49},
  pages={57–64. },
  year={2004},
}
Lai Chunhui. The smallest degree sum that yields potentially $C_k$ -graphical sequences. 2004. Vol. 49. In J. Combin. Math. Combin. Comput. . pp.57–64. . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240210105218779870764.
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