An extremal problem on potentially $K_{p,1,1}$-graphic sequences

dc.creatorLai, Chunhui
dc.date2004-08-22
dc.date2006-07-07
dc.date.accessioned2026-07-07T06:38:44Z
dc.date.available2026-07-07T06:38:44Z
dc.descriptionA sequence $S$ is potentially $K_{p,1,1}$ graphical if it has a realization containing a $K_{p,1,1}$ as a subgraph, where $K_{p,1,1}$ is a complete 3-partite graph with partition sizes $p,1,1$. Let $σ(K_{p,1,1}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $σ(S)\geq σ(K_{p,1,1}, n)$ is potentially $K_{p,1,1}$ graphical. In this paper, we prove that $σ(K_{p,1,1}, n)\geq 2[((p+1)(n-1)+2)/2]$ for $n \geq p+2.$ We conjecture that equality holds for $n \geq 2p+4.$ We prove that this conjecture is true for $p=3$.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0408292
dc.identifierhttp://arxiv.org/abs/math/0408292
dc.identifierDiscrete Mathematics and Theoretical Computer Science 7(2005), 75-80
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100845
dc.subjectCombinatorics
dc.subject05C07, 05C35
dc.titleAn extremal problem on potentially $K_{p,1,1}$-graphic sequences
dc.typetext

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