An Extremal Problem On Potentially $K_{r+1}-(kP_2\bigcup tK_2)$-graphic Sequences

Details An Extremal Problem On Potentially $K_{r+1}-(kP_2\bigcup tK_2)$-graphic Sequences An Extremal Problem On Potentially $K_{r+1}-(kP_2\bigcup tK_2)$-graphic Sequences

2006-03-26

arxiv.org/abs/math/0603602v2

International Journal of Applied Mathematics & Statistics,14(2009), 30-36

Mathematics

Combinatorics

6 pages

Scientific paper

A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine $\sigma (K_{r+1}-(kP_2\bigcup tK_2), n)$ for $n\geq 4r+10, r+1 \geq 3k+2t, k+t \geq 2,k \geq 1, t \geq 0$ .

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