6-Valent Analogues of Eberhard's Theorem.
Abstract
If (p sub j) denotes the number of j-gonal faces of a planar map, it follows from Euler's theorem that the summation from j = 1 of (3 - j)(p sub j) = 6 for every connected 6-valent graph. It is proved that, conversely, given any sequence (p1,p2,...,pn) of non-negative integers satisfying this equation, there exists a connected 6-valent planar graph that has precisely (p sub j) j-gonal faces for each j not = 3. Also established is the analogous result for graphs having a 2-cell imbedding in the torus. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1973
- Accession Number
- AD0771470
Entities
People
- Joseph Zaks
Organizations
- University of Washington