Discussiones Mathematicae Graph Theory 33(2) (2013) 429-435
doi: 10.7151/dmgt.1680

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Underlying graphs of 3-quasi-transitive digraphs and 3-transitive digraphs

Ruixia Wang and Shiying Wang

School of Mathematical Sciences,
Shanxi University,
Taiyuan, Shanxi, 030006, PR China

Abstract

A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). César Hernández-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true.

Keywords: graph orientation, 3-quasi-transitive digraph, 3-transitive digraph

2010 Mathematics Subject Classification: 05C20.

References

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Received 5 November 2011
Revised 15 May 2012
Accepted 20 June 2012