Extending an extension of Grinberg's theorem

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Grinberg's well-known necessary condition for a planar graph to be Hamiltonian was extended by Shimamoto to a condition for having a 2-factor. We derive a necessary condition for a planar graph to contain a collection of n disjoint circuits, none of which separates any other two. All is done in terms of the numbers pk which denote the numbers of k-gonal faces.

Original languageEnglish
Pages (from-to)95-98
Number of pages4
JournalJournal of Combinatorial Theory. Series B
Issue number1
StatePublished - Feb 1982

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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