Arc reversals of cycles in orientations of G vertex-multiplications

Abstract

Ryser proved that any two tournaments with the same score sequence are C3-equivalent while Beineke and Moon proved the C4-equivalence for any two bipartite tournaments with the same score lists. In this paper, we extend these results to orientations of G vertex-multiplications. We focus on two main areas, namely orientations with the same score list and with score-list parity. Our main tools are extensions of the refinement technique, directed difference graph and a reduction lemma.