Maximum genus embeddings of Steiner triple systems

Authors:
Mike J. Grannell;Terry S. Griggs;Jozef Širáň
Affiliations:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK and 17 Royal Avenue, Leyland, Lancashire, PR25 1BQ, UK;Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK;Department of Mathematics, SvF, Slovak Technical University, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
European Journal of Combinatorics - Special issue: Topological graph theory II
Year:
2005

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Abstract

We prove that for n 3 every STS(n) has both an orientable and a nonorientable embedding in which the triples of the STS(n) appear as triangular faces and there is just one additional large face. We also obtain detailed results about the possible automorphisms of such embeddings.