Minimum cycle bases for direct products of K2 with complete graphs

Abstract

We construct a minimum cycle basis for the direct product K2 x Kp of two complete graphs where p > 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp x Kq for p,q > 3 [Inform. Process. Lett. 102 (2007), 214-218.