A Degree Condition for $k$-uniform Graphs

Abstract

Let $G$ be a graph of order $n\ge 4k+8$, where $k$ is a positive integer with $kn$ even and $\delta (G)>k+1$. We show that if $max\{d_G(u),d_G(v)\}>n/2$ for each pair of nonadjacent vertices $u,v$, then $G$ has a connected $[k,k+1]$-factor excluding any given edge $e$.