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On the enumeration of circular maps with given number of edges

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Abstract

A map is a closed Riemann surface S with an embedded graph G such that S \ G is homeomorphic to a disjoint union of open disks. Tutte began a systematic study of maps in the 1960s, and contemporary authors are actively developing it. We introduce the concept of circular map and establish its equivalence to the concept of map admitting a coloring of the faces in two colors. The main result is a formula for the number of circular maps with given number of edges.

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Author information

Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    M. A. Deryagina

  2. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. D. Mednykh

Authors
  1. M. A. Deryagina
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  2. A. D. Mednykh
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Correspondence to M. A. Deryagina.

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Original Russian Text Copyright © 2013 Deryagina M.A. and Mednykh A.D.

The authors were partially supported by the Russian Foundation for Basic Research (Grants 10-01-00642 and 13-01-00513), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-921.2012.1), and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009–2013 (Contract No. 8206).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 788–806, July–August, 2013.

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Deryagina, M.A., Mednykh, A.D. On the enumeration of circular maps with given number of edges. Sib Math J 54, 624–639 (2013). https://doi.org/10.1134/S0037446613040058

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