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 notion of infinite Hamiltonian graph
β Scribed by R. Halin
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 184 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Based on the terms βendβ and βcofinal spanning subtreeβ 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.
π SIMILAR VOLUMES
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In answer to a question of ErdΕs, we show that a Hamiltonian weakly-pancyclic graph of order n can have girth as large as about 2 n/ log n. In contrast to this, we show that the existence of
## Abstract The existence of an infinite graph which is not isomorphic to a proper minor of itself was proved by Oporowski. In the present note, it is shown that an analogous result holds when immersions are considered instead of minors. The question whether or not the same is true for weak immersi
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 If a graph __G__ on __n__ vertices contains a Hamiltonian path, then __G__ is reconstructible from its edgeβdeleted subgraphs for __n__ sufficiently large.