In 1982 Laborde, Payan and Xuong [Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983)] conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet [Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173] showed that the conjecture holds for digraphs with independence number two. A digraph is p-deficient if its order is exactly p more than the order of its longest paths. It follows easily from Havet’s result that for p = 1, 2 every p-deficient digraph has an independent detour transversal. This paper explores the existence of independent detour transversals in 3-deficient digraphs.
@article{bwmeta1.element.doi-10_7151_dmgt_1650,
author = {Susan van Aardt and Marietjie Frick and Joy Singleton},
title = {Independent Detour Transversals in 3-Deficient Digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {261-275},
zbl = {1291.05082},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1650}
}
Susan van Aardt; Marietjie Frick; Joy Singleton. Independent Detour Transversals in 3-Deficient Digraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 261-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1650/
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