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6-Valent analogues of Eberhard’s theorem

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Abstract

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.

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Authors and Affiliations

  1. University of Washington, Seattle, Washington, U.S.A.

    Joseph Zaks

  2. University of Haifa, Haifa, Israel

    Joseph Zaks

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  1. Joseph Zaks
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Additional information

This research was supported in part by the Office of Naval Research Grant N00014-67-0103-0003.

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Zaks, J. 6-Valent analogues of Eberhard’s theorem. Israel J. Math. 18, 19–29 (1974). https://doi.org/10.1007/BF02758126

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  • DOI: https://doi.org/10.1007/BF02758126

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