A note on vertex pancyclic oriented graphs

Citation
J. Bang-jensen et Yb. Guo, A note on vertex pancyclic oriented graphs, J GRAPH TH, 31(4), 1999, pp. 313-318
Citations number
11
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF GRAPH THEORY
ISSN journal
03649024 → ACNP
Volume
31
Issue
4
Year of publication
1999
Pages
313 - 318
Database
ISI
SICI code
0364-9024(199908)31:4<313:ANOVPO>2.0.ZU;2-4
Abstract
Let D be an oriented graph of order n greater than or equal to 9, minimum d egree at least n - 2, such that, for the choice of distinct vertices x and y, either xy is an element of E(D) or d(+)(x) + d(-)(y) greater than or equ al to n - 3. Song (J. Graph Theory 18 (1994), 461-468) proved that D is pan cyclic. In this note, we give a short proof, based on Song's result, that D is, in fact, vertex pancyclic. This also generalizes a result of Jackson ( J. Graph Theory 5 (1981), 147-157) for the existence of a hamiltonian cycle in oriented graphs, (C) 1999 John Wiley & Sons, Inc.