On signed digraphs with all cycles negative
โ Scribed by Guy Chaty
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 235 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We say that a digraph D has the odd cycle property if there exists an edge subset S such that every cycle of D has an odd number of edges from S. We give necessary and sufficient conditions for a digraph to have the odd cycle property. We also consider the analogous problem for graphs.
The least number of 3-cycles (cycles of length 3) that a hamiltonian tournament of order n can contain is n -2 (see [3]). Since each complete strongly connected digraph contains a spanning hamiltonian subtournament (see [2]), n-2 is also the least number of 3-cycles for these digraphs. In this pape
We prove that Woodall's and GhouileHouri's conditions on degrees which ensure that a digraph is Hamiltonian, also ensure that it contains the analog of a directed Hamiltonian cycle but with one edge pointing the wrong way; that is, it contains two vertices that are connected in the same direction by