Abelian 1-factorizations of complete multipartite graphs

2012/10/03 by Mathieu Bogaerts, Bogaerts, Mathieu
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1210.1078

7 pages

arxiv created 2012/10/03 · openalex publication_date 2012/10/03 · arxiv updated 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An automorphism group G of a 1-factorization of the complete multipartite graph K_{m× n} consists in permutations of the vertices of the graph mapping factors to factors. In this paper, we give a complete answer to the existence or non-existence problem of a 1-factorization of K_{m× n} admitting an abelian group acting sharply transitively on the vertices of the graph.

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