6-Valent analogues of Eberhard's theorem

Research output: Contribution to journalArticlepeer-review

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 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
Volume18
Issue number1
DOIs
StatePublished - Dec 1974

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of '6-Valent analogues of Eberhard's theorem'. Together they form a unique fingerprint.

Cite this