# Independent transversals of longest paths in locally semicomplete and locally transitive digraphs

Hortensia Galeana-Sánchez; Ricardo Gómez; Juan José Montellano-Ballesteros

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 3, page 469-480
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, Ricardo Gómez, and Juan José Montellano-Ballesteros. "Independent transversals of longest paths in locally semicomplete and locally transitive digraphs." Discussiones Mathematicae Graph Theory 29.3 (2009): 469-480. <http://eudml.org/doc/271050>.

@article{HortensiaGaleana2009,

abstract = {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.},

author = {Hortensia Galeana-Sánchez, Ricardo Gómez, Juan José Montellano-Ballesteros},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {independent set; longest path; locally semicomplete; locally transitive},

language = {eng},

number = {3},

pages = {469-480},

title = {Independent transversals of longest paths in locally semicomplete and locally transitive digraphs},

url = {http://eudml.org/doc/271050},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

AU - Ricardo Gómez

AU - Juan José Montellano-Ballesteros

TI - Independent transversals of longest paths in locally semicomplete and locally transitive digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 3

SP - 469

EP - 480

AB - 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.

LA - eng

KW - independent set; longest path; locally semicomplete; locally transitive

UR - http://eudml.org/doc/271050

ER -

## References

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- [8] M. Frick, S. Van Aardt, J. Dunbar, M. Nielsen and O. Oellermann, A traceability conjecture for oriented graphs, The Electronic Journal of Combinatorics 15 (2008) #R150. Zbl1178.05046
- [9] H. Galeana-Sánchez and R. Gómez, Independent sets and non-augmentable paths in generalization of tournaments, Discrete Math. 308 (2008) 2460-2472, doi: 10.1016/j.disc.2007.05.016. Zbl1147.05042
- [10] J.M. Laborde, C. Payan and N.H. Xuong, Independent sets and longest paths in digraphs, in: Graphs and other combinatorial topics, Proceedings of the Third Czechoslovak Symposium of Graph Theory (1982) 173-177.

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