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 \(r\), \(1 \leq r \leq k-1\).