A Note on the Edge-Connectivity of 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 smallest possible number of vertices. In this paper we prove that $(k;g)$-cages are $k$-edge-connected if $k \geq 3$ and $g$ is odd.