Independent Detour Transversals in 3-Deficient Digraphs

• Autorzy: Susan van Aardt , Marietjie Frick , Joy Singleton
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

longest path; independent set; detour transversal; strong digraph; oriented graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 261-275

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Susan van Aardt

• Department of Mathematical Sciences University of South Africa P.O. Box 392, Unisa, 0003, South Africa

autor

Marietjie Frick

• Department of Mathematical Sciences University of South Africa P.O. Box 392, Unisa, 0003, South Africa

autor

Joy Singleton

• Department of Mathematical Sciences University of South Africa P.O. Box 392, Unisa, 0003, South Africa

Bibliografia

• [1] S.A. van Aardt, G. Dlamini, J. Dunbar, M. Frick, and O. Oellermann, The directed path partition conjecture, Discuss. Math. Graph Theory 25 (2005) 331-343. doi:10.7151/dmgt.1286[Crossref]
• [2] S.A. van Aardt, J.E. Dunbar, M. Frick, P. Katreniˇc, M.H. Nielsen, and O.R. Oellermann, Traceability of k-traceable oriented graphs, Discrete Math. 310 (2010) 1325-1333. doi:10.1016/j.disc.2009.12.022[WoS][Crossref]
• [3] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, London, 2001).
• [4] J. Bang-Jensen, M.H. Nielsen and A. Yeo, Longest path partitions in generalizations of tournaments, Discrete Math. 306 (2006) 1830-1839. doi:10.1016/j.disc.2006.03.063[Crossref]
• [5] J.A. Bondy, Basic graph theory: Paths and circuits, in: Handbook of Combinatorics, R.L. Graham, M. Gr¨otschel and L. Lov´asz (Ed(s)), (The MIT Press, Cambridge, MA, 1995) Vol I, p. 20.
• [6] P. Camion, Chemins et circuits hamiltoniens des graphes complets, C.R. Acad. Sci. Paris 249 (1959) 2151-2152.
• [7] C.C. Chen and P. Manalastas Jr., Every finite strongly connected digraph of stability 2 has a Hamiltonian path, Discrete Math. 44 (1983) 243-250. doi:10.1016/0012-365X(83)90188-7
• [8] H. Galeana-Sánchez and R. Gómez, Independent sets and non-augmentable paths in generalizations of tournaments, Discrete Math. 308 (2008) 2460-2472. doi:10.1016/j.disc.2007.05.016[Crossref][WoS]
• [9] H. Galeana-Sánchez and H.A. Rincón-Mejía, Independent sets which meet all longest paths, Discrete Math. 152 (1996) 141-145. doi:10.1016/0012-365X(94)00261-G[Crossref]
• [10] F. Havet, Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173. doi:10.1016/j.disc.2004.07.013[Crossref]
• [11] J.M. Laborde, C. Payan, N.H. Xuong, Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983).
• [12] M. Richardson, Solutions of irreflexive relations, Ann. of Math. 58 (1953) 573-590. doi:10.2307/1969755[Crossref]

Identyfikatory

DOI

10.7151/dmgt.1650