Displaying similar documents to “Independent transversals of longest paths in locally semicomplete and locally transitive digraphs”

On independent sets and non-augmentable paths in directed graphs

H. Galeana-Sánchez (1998)

Discussiones Mathematicae Graph Theory

Similarity:

We investigate sufficient conditions, and in case that D be an asymmetrical digraph a necessary and sufficient condition for a digraph to have the following property: "In any induced subdigraph H of D, every maximal independent set meets every non-augmentable path". Also we obtain a necessary and sufficient condition for any orientation of a graph G results a digraph with the above property. The property studied in this paper is an instance of the property of a conjecture of J.M. Laborde,...

Independent Detour Transversals in 3-Deficient Digraphs

Susan van Aardt, Marietjie Frick, Joy Singleton (2013)

Discussiones Mathematicae Graph Theory

Similarity:

In 1982 Laborde, Payan and Xuong [Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983)] conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet [Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173] showed that the conjecture holds for digraphs with independence number two. A digraph...

Some Results on 4-Transitive Digraphs

Patricio Ricardo García-Vázquez, César Hernández-Cruz (2017)

Discussiones Mathematicae Graph Theory

Similarity:

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. A 2-transitive digraph is a transitive digraph in the usual sense. A subset N of V is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and...

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

Ruixia Wang, Shiying Wang (2013)

Discussiones Mathematicae Graph Theory

Similarity:

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.

Kernels in monochromatic path digraphs

Hortensia Galeana-Sánchez, Laura Pastrana Ramírez, Hugo Alberto Rincón Mejía (2005)

Discussiones Mathematicae Graph Theory

Similarity:

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and (ii) for each vertex x ∈...

γ-Cycles And Transitivity By Monochromatic Paths In Arc-Coloured Digraphs

Enrique Casas-Bautista, Hortensia Galeana-Sánchez, Rocío Rojas-Monroy (2013)

Discussiones Mathematicae Graph Theory

Similarity:

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui ≠ uj if i ≠ j and for every i ∈ 0, 1, . . . , n there is a uiui+1-monochromatic path in D and there is no ui+1ui-monochromatic path in D (the...

Monochromatic paths and monochromatic sets of arcs in quasi-transitive digraphs

Hortensia Galeana-Sánchez, R. Rojas-Monroy, B. Zavala (2010)

Discussiones Mathematicae Graph Theory

Similarity:

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. We call the digraph D an m-coloured digraph if each arc of D is coloured by an element of {1,2,...,m} where m ≥ 1. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if there is no monochromatic path between two vertices of N and if for every vertex v not in N there is a monochromatic path from v...