6-Valent analogues of Eberhard's theorem

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It is shown that for every sequence of non-negative integers (p n|1≦n≠3) satisfying the equation {ie19-1} (respectively, =0) there exists a 6-valent, planar (toroidal, respectively) multi-graph that has precisely p n n gonal faces for all n, 1≦n≠3. This extends Eberhard's theorem that deals, in a similar fashion, with 3-valent, 3-connected planar graphs; the equation involved follows from the famous Euler's equation.

Original languageEnglish
Pages (from-to)19-29
Number of pages11
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Dec 1974

ASJC Scopus subject areas

  • General Mathematics


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