On k-Transitive Closures of Directed Paths
Author(s)
Krzysztof Pszczoła*
ABSTRACT
In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a graph.
In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a graph.
Cite this paper
Pszczoła, K. (2015) On k-Transitive Closures of Directed Paths. Advances in Pure Mathematics, 5, 733-737. doi: 10.4236/apm.2015.512066.
Pszczoła, K. (2015) On k-Transitive Closures of Directed Paths. Advances in Pure Mathematics, 5, 733-737. doi: 10.4236/apm.2015.512066.
References
[1] Kelly, D. (1985) Comparability Graphs. In: Rival, I., Ed., Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and Its Applications, North Holland, Dordrecht, 3-40.
http://dx.doi.org/10.1007/978-94-009-5315-4_1 [2] Gyárfás, A., Jacobson, M.S. and Kinch, L.F. (1988) On a Generalization of Transitivity for Digraphs. Discrete Mathematics, 69, 35-41.
http://dx.doi.org/10.1016/0012-365X(88)90175-6 [3] Tuza, Z. (1994) Characterization of (m,1)-Transitive and (3,2)-Transitive Semi-Complete Directed Graphs. Discrete Mathematics, 135, 335-347.
http://dx.doi.org/10.1016/0012-365X(94)00060-V [4] Hernández-Cruz, C. (2012) 3-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 32, 205-219.
http://dx.doi.org/10.7151/dmgt.1613 [5] Hernández-Cruz, C. and Montellano-Ballesteros, J.J. (2014) Some Remarks on the Structure of Strong k-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 34, 651-671.
http://dx.doi.org/10.7151/dmgt.1765
[1] Kelly, D. (1985) Comparability Graphs. In: Rival, I., Ed., Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and Its Applications, North Holland, Dordrecht, 3-40.
http://dx.doi.org/10.1007/978-94-009-5315-4_1 [2] Gyárfás, A., Jacobson, M.S. and Kinch, L.F. (1988) On a Generalization of Transitivity for Digraphs. Discrete Mathematics, 69, 35-41.
http://dx.doi.org/10.1016/0012-365X(88)90175-6 [3] Tuza, Z. (1994) Characterization of (m,1)-Transitive and (3,2)-Transitive Semi-Complete Directed Graphs. Discrete Mathematics, 135, 335-347.
http://dx.doi.org/10.1016/0012-365X(94)00060-V [4] Hernández-Cruz, C. (2012) 3-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 32, 205-219.
http://dx.doi.org/10.7151/dmgt.1613 [5] Hernández-Cruz, C. and Montellano-Ballesteros, J.J. (2014) Some Remarks on the Structure of Strong k-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 34, 651-671.
http://dx.doi.org/10.7151/dmgt.1765