Israel Journal of Mathematics

, Volume 18, Issue 1, pp 19–29 | Cite as

6-Valent analogues of Eberhard’s theorem

  • Joseph Zaks


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 preciselyp n n gonal faces for alln, 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.


Planar Graph Medial Graph Infinite Graph Connected Planar Graph Apply Operation 
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Copyright information

© The Weizmann Science Press of Israel 1974

Authors and Affiliations

  • Joseph Zaks
    • 1
    • 2
  1. 1.University of WashingtonSeattleU.S.A.
  2. 2.University of HaifaHaifaIsrael

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