On $[a,b]$-Covered Graphs

Abstract

A graph $G$ is $[a,b]$-covered if each edge of $G$ belongs to an $[a,b]$-factor. Here, a necessary and sufficient condition for a graph to be $[a,b]$-covered is given, and it is shown that an $[m,n]$-graph is $[a,b]$-covered if $bm–na\ge 2(n-b)$ and $0\le a<b\le n$.