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 language | English |
---|---|
Pages (from-to) | 19-29 |
Number of pages | 11 |
Journal | Israel Journal of Mathematics |
Volume | 18 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1974 |
ASJC Scopus subject areas
- General Mathematics