Enumeration of Hamiltonian cycles in certain generalized Petersen graphs
β Scribed by Allen J Schwenk
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 497 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
The problem is considered under which conditions a 4-connected planar or projective planar graph has a Hamiltonian cycle containing certain prescribed edges and missing certain forbidden edges. The results are applied to obtain novel lower bounds on the number of distinct Hamiltonian cycles that mus
In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are
## Abstract We construct 3βregular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ β __V__(__C__~1~). By a similar construction we obtain loopless 4βregular graphs having precisely one hamiltonian cycle. The basis for these const