Triangular Embeddings

Authors:
M. J. Grannell;M. Knor
Affiliations:
Department of Mathematics and Statistics, the Open University, Walton hall, Milton keynes MK7 6AA, United Kingdom;Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
Journal of Graph Theory
Year:
2012

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Abstract

We prove that for every prime number p and odd m1, as s→∞, there are at least w face 2-colorable triangular embeddings of Kw, w, w, where w = m·ps. For both orientable and nonorientable embeddings, this result implies that for infinitely many infinite families of z, there is a constant c0 for which there are at least z nonisomorphic face 2-colorable triangular embeddings of Kz. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc. (Contract grant sponsor: Slovak Research Grants; Contract grant numbers: VEGA 1/0489/08; APVV-0040-06; APVV-0104-07 (to M. K.).)