An extremal problem on potentially $K_{m}-C_{4}$-graphic sequences

dc.creatorLai, Chunhui
dc.date2004-09-03
dc.date2006-07-07
dc.date.accessioned2026-07-07T08:26:31Z
dc.date.available2026-07-07T08:26:31Z
dc.descriptionA sequence $S$ is potentially $K_{m}-C_{4}$-graphical if it has a realization containing a $K_{m}-C_{4}$ as a subgraph. Let $σ(K_{m}-C_{4}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $σ(S)\geq σ(K_{m}-C_{4}, n)$ is potentially $K_{m}-C_{4}$-graphical. In this paper, we prove that $σ(K_{m}-C_{4}, n)\geq (2m-6)n-(m-3)(m-2)+2,$ for $n \geq m \geq 4.$ We conjecture that equality holds for $n \geq m \geq 4.$ We prove that this conjecture is true for $m=5$.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0409041
dc.identifierhttp://arxiv.org/abs/math/0409041
dc.identifierJournal of Combinatorial Mathematics and Combinatorial Computing, 61 (2007), 59-63.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136966
dc.subjectCombinatorics
dc.subject05C07, 05C35
dc.titleAn extremal problem on potentially $K_{m}-C_{4}$-graphic sequences
dc.typetext

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