Camino Balbuena
A (,
)-cage is a
-regular graph with girth
and with
the least possible number of vertices. It has been proved that every
-cage with
is 3-connected [See the papers by M.
Daven and C. A. Rodger,
-cages are
-connected, Discrete
Math. 199 (1999), 207-215; or the paper by T. Jiang and D. Mubayi,
Connectivity and separating sets of cages, Journal of Graph Theory
29 (1998), 35-44].
In this work we prove that all (,
)-cages are
-connected with
for
odd. This result supports the conjecture
of Fu, Huang and Rodger that all
-cages are
-connected.