Strongly Pan-Factorial Property in Cages

Abstract

A $(k;g)$-graph is a $k$-regular graph with girth $g$. A $(k;g)$-cage is a $(k;g)$-graph with the least number of vertices. In this note, we show that a $(k;g)$-cage has an $r$-factor of girth at least $g$ containing or avoiding a given edge for all $r$, $1\le r\le k-1$.