The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap
On the hamiltonian index of a graph
✍ Scribed by Marko LovrečičSaražin
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 217 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## An extension of CI theorem of Chamhnd and Wall is obtained and, with it, a bound on the lamiltoniau index h(G) of a connected graph G (other than a path) is determined. As a tonsequence, it is Fhown that if G is homogeneously traceable, then h(Gj ~2.
## Abstract Based on the terms “end” and “cofinal spanning subtree” a general notion of Hamiltonicity of infinite graphs is developed. It is shown that the cube of every connected locally finite graph is Hamiltonian in this generalized sense.
It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial-time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the co
## 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__‐vertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ ≥ 12. We also pro