Solution on strong partition of 2-balanced regular multipartite tournaments

2024/03/13 by Jiangdong Ai, Ai, Jiangdong, Fankang He +3
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2403.08351

openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We call a partition of a c-partite tournament into tournaments of order c is strong if each tournament is strongly connected. The strong partition number denoted as ST(r), represents the minimum integer c' such that every regular r-balanced c-partite tournament has a strong partition with c≥ c'. Figueroa, Montellano-Ballesteros and Olsen showed the existence of ST(r) for all r≥ 2 and proved that 5≤ ST(2)≤ 7. In this note, we establish that ST(2)=6 and we also show the unique 2-balanced 5-partite tournament which has no strong partition.

Related

• Decomposition of balanced multipartite tournaments into strongly\n connected tournaments
• Partitioning a tournament into sub-tournaments of high connectivity
• Bipartitions of highly connected tournaments
• The existence of partitioned balanced tournament designs
• Conditions on the regularity of balanced c-partite tournaments for the existence of strong subtournaments with high minimum degree