Independent Detour Transversals in 3-Deficient Digraphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 261.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 05C20, 05C38
Mots-clés : longest path, independent set, detour transversal, strong digraph, oriented graph 
@article{DMGT_2013__33_2_268060,
     author = {Susan van Aardt and Marietjie Frick and Joy Singleton},
     title = {Independent {Detour} {Transversals} in {3-Deficient} {Digraphs}},
     journal = {Discussiones Mathematicae Graph Theory},
     pages = {261},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2013},
     zbl = {1291.05082},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268060/}
}
TY  - JOUR
AU  - Susan van Aardt
AU  - Marietjie Frick
AU  - Joy Singleton
TI  - Independent Detour Transversals in 3-Deficient Digraphs
JO  - Discussiones Mathematicae Graph Theory
PY  - 2013
SP  - 261
VL  - 33
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268060/
LA  - en
ID  - DMGT_2013__33_2_268060
ER  - 
%0 Journal Article
%A Susan van Aardt
%A Marietjie Frick
%A Joy Singleton
%T Independent Detour Transversals in 3-Deficient Digraphs
%J Discussiones Mathematicae Graph Theory
%D 2013
%P 261
%V 33
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268060/
%G en
%F DMGT_2013__33_2_268060
Susan van Aardt; Marietjie Frick; Joy Singleton. Independent Detour Transversals in 3-Deficient Digraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 261. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268060/