Some Remarks On The Structure Of Strong K-Transitive Digraphs

• Autorzy: César Hernández-Cruz , Juan José Montellano-Ballesteros
• Języki publikacji: EN

Abstrakty

EN

A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong k-transitive digraphs having a cycle of length at least k. We show that in most cases, such digraphs are complete digraphs or cycle extensions. Also, the obtained results are used to prove some particular cases of the Laborde-Payan-Xuong Conjecture.

Słowa kluczowe

EN

digraph; transitive digraph; k-transitive digraph; quasi-transitive digraph; k-quasi-transitive digraph; Laborde-Payan-Xuong Conjecture.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 651-671

Daty

wydano

2014-11-01

otrzymano

2012-05-07

poprawiono

2013-07-15

zaakceptowano

2013-08-06

online

2014-11-15

Twórcy

autor

César Hernández-Cruz

• Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria, México, D.F., C.P. 04510, México

autor

Juan José Montellano-Ballesteros

• Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria, México, D.F., C.P. 04510, México

Bibliografia

• [1] J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications (Springer-Verlag Berlin, Heidelberg New York, 2002).
• [2] R. Diestel, Graph Theory 3rd Edition (Springer-Verlag Berlin, Heidelberg New York, 2005).
• [3] H. Galeana-Sánchez and C. Hernández-Cruz, k-kernels in k-transitive and k-quasi- transitive digraphs, Discrete Math. 312 (2012) 2522-2530. doi:10.1016/j.disc.2012.05.005
• [4] A. Ghouila-Houri, Caract´erisation des graphes non orient´es dont on peut orienterles arrˆetes de mani`ere `a obtenir le graphe d’une relation d’ordre, C. R. Acad. Sci. Paris 254 (1962) 1370-1371.
• [5] C. Hernández-Cruz, 3-transitive digraphs, Discuss. Math. Graph Theory 32 (2012) 205-219. doi:10.7151/dmgt.1613
• [6] C. Hernández-Cruz, 4-transitive digraphs I: The structure of strong 4-transitive di- graphs, Discuss. Math. Graph Theory 33 (2013) 247-260. doi:10.7151/dmgt.1645
• [7] J.M. Laborde, C. Payan and N.H. Xuong, Independent sets and longest directed paths in digraphs, in: Graphs and other Combinatorial Topics, Prague, M. Fiedler (Ed(s)), (Teubner, Leipzig, 1983) 173-177.
• [8] R. Wang, A conjecture on k-transitive digraphs, Discrete Math. 312 (2012) 1458-1460. doi:0.1016/j.disc.2012.01.011
• [9] R. Wang and S. Wang, Underlying graphs of 3-quasi-transitive digraphs and 3- transitive digraphs, Discuss. Math. Graph Theory 33 (2013) 429-436. doi:10.7151/dmgt.1680

Identyfikatory

DOI

10.7151/dmgt.1765