An extremal problem on potentially $K_{m}-P_{k}$-graphic sequences
| dc.creator | Lai, Chunhui | |
| dc.date | 2004-09-24 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T06:38:50Z | |
| dc.date.available | 2026-07-07T06:38:50Z | |
| dc.description | A sequence $S$ is potentially $K_{m}-P_{k}$ graphical if it has a realization containing a $K_{m}-P_{k}$ as a subgraph. Let $σ(K_{m}-P_{k}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $σ(S)\geq σ(K_{m}-P_{k}, n)$ is potentially $K_{m}-P_{k}$ graphical. In this paper, we prove that $σ(K_{m}-P_{k}, n)\geq (2m-6)n-(m-3)(m-2)+2,$ for $n \geq m \geq k+1\geq 4.$ We conjecture that equality holds for $n \geq m \geq k+1\geq 4.$ We prove that this conjecture is true for $m=k+1=5$ and $m=k+2=5$. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409466 | |
| dc.identifier | http://arxiv.org/abs/math/0409466 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100879 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C07, 05C35 | |
| dc.title | An extremal problem on potentially $K_{m}-P_{k}$-graphic sequences | |
| dc.type | text |