Discussiones Mathematicae Graph Theory 29(3) (2009) 469-480
doi: 10.7151/dmgt.1458

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Hortensia Galeana-Sánchez,  Ricardo Gómez and Juan José Montellano-Ballesteros

Instituto de Matemáticas de la Universidad Nacional Autónoma de México
Circuito Exterior, Ciudad Universitaria
C.P. 04510, México D.F., México


We present several results concerning the Laborde-Payan-Xuang conjecture stating that in every digraph there exists an independent set of vertices intersecting every longest path. The digraphs we consider are defined in terms of local semicompleteness and local transitivity. We also look at oriented graphs for which the length of a longest path does not exceed 4.

Keywords: independent set, longest path, locally semicomplete, locally transitive.

2000 Mathematics Subject Classification: 05C20, 05C38.


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Received 26 October 2007
Revised 15 May 2009
Accepted15 May 2009