An Extremal Problem On Potentially $K_{r+1}-(k{P}_2\bigcup t{K}_2)$-graphic Sequences

Abstract

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 $\sigma (S)\ge \sigma (K_m-H,n)$ is potentially $K_m-H$-graphical. In this paper, we determine $\sigma (K_{r+1}-(k{P}_2\bigcup t{K}_2),n)$ for $n\ge 4r+10,r+1\ge 3k+2t,k+t\ge 2,k\ge 1,t\ge 0$ .

6 pages

References in corpus (1)

• A note on potentially $K_4-e$ graphical sequences