On minimally 3-connected graphs on a surface

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Abstract

It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

Original languageEnglish
Pages (from-to)760
Number of pages1
JournalElectronic Notes in Discrete Mathematics
Volume11
DOIs
Publication statusPublished - 2002 Jul
Externally publishedYes

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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