An extremal problem on potentially $K_{p_{1},p_{2},...,p_{t}}$-graphic sequences

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dc.creatorLai, Chunhui
dc.date2004-08-24
dc.date.accessioned2026-07-07T05:11:30Z
dc.date.available2026-07-07T05:11:30Z
dc.descriptionA sequence $S$ is potentially $K_{p_{1},p_{2},...,p_{t}}$ graphical if it has a realization containing a $K_{p_{1},p_{2},...,p_{t}}$ as a subgraph, where $K_{p_{1},p_{2},...,p_{t}}$ is a complete t-partite graph with partition sizes $p_{1},p_{2},...,p_{t} (p_{1}\geq p_{2}\geq ...\geq p_{t} \geq 1)$. Let $σ(K_{p_{1},p_{2},...,p_{t}}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $σ(S)\geq σ(K_{p_{1},p_{2},...,p_{t}}, n)$ is potentially $K_{p_{1},p_{2},...,p_{t}}$ graphical. In this paper, we prove that $σ(K_{p_{1},p_{2},...,p_{t}}, n)\geq 2[((2p_{1}+2p_{2}+...+2p_{t}-p_{1}-p_{2}-...-p_{i}-2)n -(p_{1}+p_{2}+...+p_{t}-p_{i})(p_{i}+p_{i+1}+...+p_{t}-1)+2)/2]$ for $n \geq p_{1}+p_{2}+...+p_{t}, i=2,3,...,t.$
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/math/0408326
dc.identifierhttp://arxiv.org/abs/math/0408326
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72266
dc.subjectCombinatorics
dc.subject05C07, 05C35
dc.titleAn extremal problem on potentially $K_{p_{1},p_{2},...,p_{t}}$-graphic sequences
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