Abelian 1-factorizations of complete multipartite graphs

Mathieu Bogaerts

Abelian 1-factorizations of complete multipartite graphs

Combinatorics 2012-10-04 v1

Authors: Mathieu Bogaerts

Abstract

An automorphism group G of a 1-factorization of the complete multipartite graph $K_{m\times n}$ 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 $K_{m\times n}$ admitting an abelian group acting sharply transitively on the vertices of the graph.

Keywords

automorphism groups algebraic group actions abelian groups

Cite

@article{arxiv.1210.1078,
  title  = {Abelian 1-factorizations of complete multipartite graphs},
  author = {Mathieu Bogaerts},
  journal= {arXiv preprint arXiv:1210.1078},
  year   = {2012}
}

Comments

7 pages

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