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A tight lower bound on the maximum genus of a 3-connected loopless multigraph

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Abstract

It is proved that every 3-connected loopless multigraph has maximum genus at least one-third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten, it is upper-embeddable. This lower bound is tight. There are infinitely many 3-connected loopless multigraphs attaining this bound.

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Authors and Affiliations

  1. Dept. of Math., Capital Normal Univ., 100037, Beijing

    Li Deming & Liu Yanpei

  2. Dept of Math., Norhtern Jiaotong Univ., 100044, Beijing

    Li Deming & Liu Yanpei

Authors
  1. Li Deming
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  2. Liu Yanpei
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Deming, L., Yanpei, L. A tight lower bound on the maximum genus of a 3-connected loopless multigraph. Appl. Math. Chin. Univ. 15, 369–376 (2000). https://doi.org/10.1007/s11766-000-0032-5

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  • DOI: https://doi.org/10.1007/s11766-000-0032-5

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