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

2024/02/03 by Myung‐Ho Choi, Choi, Myungho, Suh-Ryung Kim +1
Business, Management and Accounting · Engineering · #05C20 #05C75 #Combinatorics (math.CO) #Digital Platforms and Economics #FOS: Mathematics #ICT Impact and Policies

paper · pdf · doi:10.48550/arxiv.2402.01986

openalex publication_date 2024/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the previous paper titled "On (1,2)-step competition graphs of multipartite tournaments" \citechoi202412step we completely characterize C_1,2(D) for a tight multipartite tournament D. As an extension, in this paper, we study (1,2)-step competition graphs of multipartite tournaments that are not tight, which will be called loose. For a loose multipartite tournament D, various meaningful results are obtained in terms of C_1,2(D) being interval and C_1,2(D) being connected.

Related

• On (1,2)-step competition graphs of multipartite tournaments
• On (1,2)-step competition graphs of bipartite tournaments
• Multipartite tournaments in which any two vertices have an (i,j)-step common out-neighbor
• On m-step competition graphs of bipartite tournaments
• The triangle-free graphs which are competition graphs of multipartite tournaments