On (1,2)-step competition graphs of multipartite tournaments

2024/01/31 by Choi, Myungho, Kim, Suh-Ryung
#05C20 #05C75 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.17817

Abstract

A multipartite tournament is an orientation of a complete k-partite graph for some positive integer k≥ 3. We say that a multipartite tournament D is tight if every partite set forms a clique in the (1,2)-step competition graph, denoted by C_1,2(D), of D. In this paper, we completely characterize C_1,2(D) for a tight multipartite tournament D. We will study C_1,2(D) for a multipartite tournament D that is not tight in a follow up paper.

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