New results on connectivity of cages

An (r,g)-cage is an r-regular graph of girth g of minimum order. We prove that all (r,g)-cages are at least (⌊r/2⌋+1)-connected for every odd girth g⩾7, by means of a matrix technique which allows us to construct graphs without short cycles. This lower bound on the vertex connectivity of cages is a new advance in proving the conjecture of Fu, Huang and Rodger which states that all (r,g)-cages are r-connected.