Geodesic
On independent sets and non-augmentable paths in directed graphs
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 171-181

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We investigate sufficient conditions, and in case that D be an asymmetrical digraph a necessary and sufficient condition for a digraph to have the following property: "In any induced subdigraph H of D, every maximal independent set meets every non-augmentable path". Also we obtain a necessary and sufficient condition for any orientation of a graph G results a digraph with the above property. The property studied in this paper is an instance of the property of a conjecture of J.M. Laborde, Ch. Payan and N.H. Huang: "Every digraph contains an independent set which meets every longest directed path" (1982).
Keywords: digraph, independent set, directed path, non-augmentable path 
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Galeana-Sánchez, H. On independent sets and non-augmentable paths in directed graphs. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 171-181. http://geodesic.mathdoc.fr/item/DMGT_1998_18_2_a3/