Pairs of Hamiltonian circuits in 5-connected planar graphs

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Settling a problem raised by B. Grünbaum, J. Malkevitch, and the author, we present 5-valent 5-connected planar graphs that admit no pairs of edgedisjoint Hamiltonian circuits; our smallest example has 176 vertices. This is used to construct an infinite family of 5-valent 5-connected planar graphs, in which every member has the property that any pair of Hamiltonian circuits in it share at least about 1 168 of their edges. We construct 4- and 5-valent, 3-connected non-Hamiltonian planar graphs.

Original languageEnglish
Pages (from-to)116-131
Number of pages16
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Oct 1976

ASJC Scopus subject areas

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


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