Improved lower bound for the vertex connectivity of (δ;g)-cages

A (δ,g)-cage is a δ-regular graph with girth g and with the least possible number of vertices. We prove that all (δ,g)-cages are r-connected with r⩾δ+1 for g⩾7 odd. This result supports the conjecture of Fu, Huang and Rodger that all (δ;g)-cages are δ-connected.