An extremal problem on potentially $K_{p,1,1}$-graphic sequences
| dc.creator | Lai, Chunhui | |
| dc.date | 2004-08-22 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T06:38:44Z | |
| dc.date.available | 2026-07-07T06:38:44Z | |
| dc.description | A 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.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408292 | |
| dc.identifier | http://arxiv.org/abs/math/0408292 | |
| dc.identifier | Discrete Mathematics and Theoretical Computer Science 7(2005), 75-80 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100845 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C07, 05C35 | |
| dc.title | An extremal problem on potentially $K_{p,1,1}$-graphic sequences | |
| dc.type | text |