## Abstract We obtain several sufficient conditions on the degrees of an oriented graph for the existence of long paths and cycles. As corollaries of our results we deduce that a regular tournament contains an edgeβdisjoint Hamilton cycle and path, and that a regular bipartite tournament is hamilto
Long paths and cycles in tough graphs
β Scribed by H. J. Broersma; J. van den Heuvel; H. A. Jung; H. J. Veldman
- Publisher
- Springer Japan
- Year
- 1993
- Tongue
- English
- Weight
- 575 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
In this article, we establish bounds for the length of a longest cycle C in a 2-connected graph G in terms of the minimum degree Ξ΄ and the toughness t. It is shown that C is a Hamiltonian cycle or |C| β₯ (t + 1)Ξ΄ + t.
## Abstract Let __G__ be a graph and __T__ a set of vertices. A __Tβpath__ in __G__ is a path that begins and ends in __T__, and none of its internal vertices are contained in __T__. We define a __Tβpath covering__ to be a union of vertexβdisjoint __T__βpaths spanning all of __T__. Concentrating on