Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs

• Autorzy: Ruixia Wang , Shiying Wang
• Języki publikacji: EN

Abstrakty

EN

A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar Hern´andez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true.

Słowa kluczowe

EN

graph orientation; 3-quasi-transitive digraph; 3-transitive digraph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 429-435

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Ruixia Wang

• School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, PR China

autor

Shiying Wang

• School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, PR China

Bibliografia

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• [2] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer, London, 2000).
• [3] C. Hernández-Cruz, 3-transitive digraphs, Discuss. Math. Graph Theory 32 (2012) 205-219. doi:10.7151/dmgt.1613[Crossref]
• [4] A. Ghouila-Houri, Caractérization des graphes non orient´es dont onpeut orienter les arrˆetes de mani`ere `aobtenir le graphe dune relation dordre, Comptes Rendus de l’Acad´emie des Sciences Paris 254 (1962) 1370-1371.
• [5] H. Galeana-Sánchez, I.A. Goldfeder and I. Urrutia, On the structure of strong 3- quasi-transitive digraphs, Discrete Math. 310 (2010) 2495-2498. doi:10.1016/j.disc.2010.06.008[WoS][Crossref]
• [6] H. Galeana-Sánchez and C. Hernández-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]
• [7] S.Wang and R.Wang, Independent sets and non-augmentable paths in arc-locally insemicomplete digraphs and quasi-arc-transitive digraphs, Discrete Math. 311 (2011) 282-288. doi:10.1016/j.disc.2010.11.009[WoS][Crossref]

Identyfikatory

DOI

10.7151/dmgt.1680