Conditions are given for the existence of hamiltonian paths and cycles in the so-called Toeplitz graphs, i.e. simple graphs with a symmetric Toeplitz adjacency matrix.
On hamiltonian Toeplitz graphs
β Scribed by Clemens Heuberger
- Book ID
- 108315647
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 332 KB
- Volume
- 245
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
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.
## 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.