Let D be an oriented graph of order n β₯ 9, minimum degree at least n -2, such that, for the choice of distinct vertices x and y, . Graph Theory 18 (1994), 461-468) proved that D is pancyclic. In this note, we give a short proof, based on Song's result, that D is, in fact, vertex pancyclic. This also
Pancyclic out-arcs of a vertex in oriented graphs
β Scribed by Qiaoping Guo; Shengjia Li; Ruijuan Li; Gaokui Xu
- Book ID
- 116577143
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 136 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract An arc leaving a vertex x in a digraph is called an outβarc of x. Thomassen (J Combin Theory Ser B 28 (1980), 142β163) proved that every strong tournament contains a vertex whose every outβarc is contained in a Hamiltonian cycle. In 2000, Yao et al. (Discrete Appl Math 99 (2000), 245β24
We apply proof techniques developed by L. Lovasz and A. Frank to obtain several results on the arc-connectivity of graphs and digraphs. The first results concern the operation of splitting two arcs from a vertex of an Eulerian graph or digraph in such a way as to preserve local connectivity conditio