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Wong, H. W. W., & Tay, E. G. (2022). Arc reversals of cycles in orientations of G vertex-multiplications. Discrete Mathematics, 345(10), Article 112999. https://doi.org/10.1016/j.disc.2022.112999
Ryser proved that any two tournaments with the same score sequence are -equivalent while Beineke and Moon proved the -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.
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