Contract grant sponsor: CNPq; Contract grant number: Proc. 500016/2010-2)
Quasi-Random Oriented Graphs
Article first published online: 17 OCT 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 2, pages 198–209, October 2013
How to Cite
Griffiths, S. (2013), Quasi-Random Oriented Graphs. J. Graph Theory, 74: 198–209. doi: 10.1002/jgt.21701
- Issue published online: 2 AUG 2013
- Article first published online: 17 OCT 2012
- Manuscript Revised: 22 AUG 2012
- Manuscript Received: 10 AUG 2011
- CNPq. Grant Number: 500016/2010-2
- oriented graphs
We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham, and Wilson  in the case of unoriented graphs, and by Chung and Graham  in the case of tournaments. Indeed, our main theorem extends to the case of a general underlying graph G, the main result of  which corresponds to the case that G is complete. One interesting aspect of these results is that exactly two of the four orientations of a four cycle can be used for a quasi-randomness condition, i.e., if the number of appearances they make in D is close to the expected number in a random orientation of the same underlying graph, then the same is true for every small oriented graph H.