Results 11 to 20 of about 4,954 (163)
Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2013 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 ...
Wang Ruixia, Wang Shiying
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Some Results on 4-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2017 Let D be a digraph with set of vertices V and set of arcs A. We say that D is k-transitive if for every pair of vertices u, v ∈ V, the existence of a uv-path of length k in D implies that (u, v) ∈ A.
García-Vázquez Patricio Ricardo +1 more
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4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2013 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).
Hernández-Cruz César
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Construction of k-arc transitive digraphs
Discrete Mathematics, 2001 A digraph is \(k\)-arc transitive if it has a group of automorphisms, which acts transitively on the set of \(k\)-arcs. The corresponding notion for undirected graphs led to remarkable results in that finite cubic graphs cannot be \(k\)-arc transitive for \(k> 5\) and that the only finite connected \(k\)-arc transitive graphs with \(k\geq 8\) are the ...
P. Mansilla, Sònia, Serra, Oriol
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(K − 1)-Kernels In Strong K-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2015 Let D = (V (D),A(D)) be a digraph and k ≥ 2 be an integer. A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v) ≥ k; it is l-absorbent if for every u ∈ V (D) − N, there exists v ∈ N such that d(u, v) ≤ l.
Wang Ruixia
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Kernels in quasi-transitive digraphs
Discrete Mathematics, 2006 In this paper \(D\) denotes a possibly infinite digraph. A kernel \(N\) of a digraph \(D\) is an independent set of vertices such that for each \(w\in V(D)-N\) there exists an arc from \(w\) to \(N\). A digraph \(D\) is quasi-transitive when \(uv\in A(D)\) and \(vw\in A(D)\) implies that \(uw\in A(D)\) or \(wu\in A(D)\).
Galeana-Sánchez, Hortensia +1 more
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Partitioning Transitive Tournaments into Isomorphic Digraphs [PDF]
Order, 2020 AbstractIn an earlier paper (see Sali and Simonyi Eur. J. Combin.20, 93–99, 1999) the first two authors have shown that self-complementary graphs can always be oriented in such a way that the union of the oriented version and its isomorphically oriented complement gives a transitive tournament.
Sali, Attila +2 more
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-TRANSITIVE DIGRAPHS PRESERVING A CARTESIAN DECOMPOSITION [PDF]
Journal of the Australian Mathematical Society, 2015 In this paper, we combine group-theoretic and combinatorial techniques to study$\wedge$-transitive digraphs admitting a cartesian decomposition of their vertex set. In particular, our approach uncovers a new family of digraphs that may be of considerable interest.
Morris, J, SPIGA, PABLO
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Some Remarks On The Structure Of Strong K-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2014 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.
Hernández-Cruz César +1 more
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On kernels by rainbow paths in arc-coloured digraphs
Open Mathematics, 2021 In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph DD, which is a subset SS of vertices of DD such that (aa) there exists no ...
Li Ruijuan, Cao Yanqin, Zhang Xinhong
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