In this paper we obtain two sufficient conditions, Ore type (Theorem 1) and Dirac type (Theorem 2). on the degrees of a bipartite oriented graph for ensuring the existence of long paths and cycles. These conditions are shown to be the best possible in a sense. An oriented graph is a digraph without
Long paths and cycles in oriented graphs
β Scribed by Bill Jackson
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 501 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
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 hamiltonian.
π SIMILAR VOLUMES
## Abstract Let __G__ be a graph of order __n__ and define __NC(G)__ = min{|__N__(__u__) βͺ __N__(__v__)| |__uv__ β __E__(__G__)}. A cycle __C__ of __G__ is called a __dominating cycle__ or __D__β__cycle__ if __V__(__G__) β __V__(__C__) is an independent set. A __D__β__path__ is defined analogously.
## Abstract A cycle __C__ in a graph __G__ is a __Hamilton cycle__ if __C__ contains every vertex of __G__. Similarly, a path __P__ in __G__ is a __Hamilton path__ if __P__ contains every vertex of __G__. We say that __G__ is __Hamilton__β__connected__ if for any pair of vertices, __u__ and __v__ o
## Abstract In this article, we apply a cutting theorem of Thomassen to show that there is a function __f__: N β N such that if __G__ is a 3βconnected graph on __n__ vertices which can be embedded in the orientable surface of genus __g__ with faceβwidth at least __f__(__g__), then __G__ contains a