Independent transversals of longest paths in locally semicomplete and transitive digraphs

Hortensia Galeana-Sánchez, Ricardo Gómez, Juan José Montellano-Ballesteros
2009 Discussiones Mathematicae Graph Theory  
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.
doi:10.7151/dmgt.1458 fatcat:nv6d6ey5trb43g3mzjm2h3cqhq