Complexity of the hamiltonian cycle in regular graph problem
β Scribed by C. Picouleau
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 491 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0304-3975
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## 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
In 1975, John Sheehan conjectured that every Hamiltonian 4-regular graph has a second Hamiltonian cycle. Combined with earlier results this would imply that every Hamiltonian r-regular graph (r 3) has a second Hamiltonian cycle. We shall verify this for r 300.