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2013 | 33 | 2 | 247-260
Tytuł artykułu

4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a long time, and recently, 3-transitive digraphs have been characterized. In this work, some general structural results are proved for k-transitive digraphs with arbitrary k ≥ 2. Some of this results are used to characterize the family of 4-transitive digraphs. Also some of the general results remain valid for k-quasi-transitive digraphs considering an additional hypothesis. A conjecture on a structural property of k-transitive digraphs is proposed.
Wydawca
Rocznik
Tom
33
Numer
2
Strony
247-260
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-04-13
Twórcy
  • Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria, México, D.F., C.P. 04510, México, cesar@matem.unam.mx
Bibliografia
  • [1] J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications (Springer-Verlag, Berlin Heidelberg New York, 2002).
  • [2] J. Bang-Jensen and J. Huang, Quasi-transitive digraphs, J. Graph Theory 20 (1995) 141-161. doi:10.1002/jgt.3190200205[Crossref]
  • [3] C. Berge, Graphs (North-Holland, Amsterdam New York, 1985).
  • [4] F. Boesch and R. Tindell, Robbins Theorem for mixed multigraphs, Amer. Math. Monthly 87 (1980) 716-719. doi:10.2307/2321858[Crossref]
  • [5] R.A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) (Cambridge University Press, 1991).
  • [6] R. Diestel, Graph Theory 3rd Edition (Springer-Verlag, Berlin Heidelberg New York, 2005).
  • [7] H. Galeana-Sánchez, I.A. Goldfeder and I. Urrutia, On the structure of 3-quasitransitive digraphs, Discrete Math. 310 (2010) 2495-2498. doi:10.1016/j.disc.2010.06.008[Crossref]
  • [8] H. Galeana-Sánchez and C. Hern´andez-Cruz, k-kernels in k-transitive and k-quasitransitive digraphs, Discrete Math. 312 (2012) 2522-2530. doi:10.1016/j.disc.2012.05.005[WoS][Crossref]
  • [9] C. Hernández-Cruz, 3-transitive digraphs, Discuss. Math. Graph Theory 32 (2012) 205-219. doi:10.7151/dmgt.1613[Crossref]
  • [10] S.Wang and R.Wang, Independent sets and non-augmentable paths in arc-locally insemicomplete digraphs and quasi-arc-transitive digraphs, Discrete Math. 311 (2010) 282-288. doi:10.1016/j.disc.2010.11.009[WoS][Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1645
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