## Abstract In this paper we show that every connected, 3βΞ³βcritical graph on more than 6 vertices has a Hamiltonian path.
On critically hamiltonian graphs
β Scribed by Linda Lesniak-Foster
- Publisher
- Akadmiai Kiad
- Year
- 1977
- Tongue
- English
- Weight
- 216 KB
- Volume
- 29
- Category
- Article
- ISSN
- 1588-2632
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π SIMILAR VOLUMES
A perfect graph is critical, if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, a
## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ β§ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ β __V__(__G__), then __G__ is hamiltonianβconnected. We generalize this result using set degrees.
Suppose G is a graph, F is a l-factor of G. G is called F-Hamiltonian, if there exists a Hamiltonian cycle containing F in G. In this paper, two necessary and sufficient conditions for a general graph and a bipartite graph being F-Hamiltonian are provided, respectively.