Geodesic
Independent transversals of longest paths in locally semicomplete and locally transitive digraphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 469-480

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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 
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     title = {Independent transversals of longest paths in locally semicomplete and locally transitive digraphs},
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Galeana-Sánchez, Hortensia; Gómez, Ricardo; Montellano-Ballesteros, Juan. Independent transversals of longest paths in locally semicomplete and locally transitive digraphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 469-480. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a1/