By a theorem of the toughness t(G) of a non-hamiitonian maximal planar graph G is less than or equal to 2. Improving a result of , it is shown that the shortness exponent of the class of maximal planar graphs with toughness greater than or equal to ~ is less than 1.
A 1-tough nonhamiltonian maximal planar graph
β Scribed by Takao Nishizeki
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 93 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
It is shown that the shortness exponent of the class of l-tough, maximal planar graphs is at most log, 5. The non-Hamiltonian, l-tough, maximal planar graph with a minimum number of vertices is presented.
graphs is at most log, 6.
Frydrych, W., All nonhamiltonian tough graphs satisfying a 3-degree sum and Fan-type conditions, Discrete Mathematics 121 (1993) 93-104. It is shown that if G is a l-tough nonhamiltonian graph on even number vertices n>4 such that d(x)+d(y)+d(z)>n for every triple of mutually distinct and nonadjace
## Abstract We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on __p__ vertices. In particular, we construct a __p__βvertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ β₯ 12. We also pro
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