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Displaying similar documents to “Exponents of two-colored digraphs”

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

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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...

Independent Detour Transversals in 3-Deficient Digraphs

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

Discussiones Mathematicae Graph Theory

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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...

Digraphs with large exponent.

Kirkland, S., Olesky, D.D., van den Driessche, P. (2000)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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γ-Cycles In Arc-Colored Digraphs

Hortensia Galeana-Sánchez, Guadalupe Gaytán-Gómez, Rocío Rojas-Monroy (2016)

Discussiones Mathematicae Graph Theory

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We call a digraph D an m-colored digraph if the arcs of D are colored with m colors. A directed path (or a directed cycle) is called monochromatic if all of its arcs are colored alike. A subdigraph H in D is called rainbow if all of its arcs have different colors. A set N ⊆ V (D) is said to be a kernel by monochromatic paths of D if it satisfies the two following conditions: for every pair of different vertices u, v ∈ N there is no monochromatic path in D between them, and for every...

Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs

Hortensia Galeana-Sánchez, R. Rojas-Monroy, B. Zavala (2009)

Discussiones Mathematicae Graph Theory

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We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. 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 for every pair of vertices of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured...

Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments

Hortensia Galeana-Sanchez, Rocío Rojas-Monroy (2008)

Discussiones Mathematicae Graph Theory

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We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. 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...

Kernels and cycles' subdivisions in arc-colored tournaments

Pietra Delgado-Escalante, Hortensia Galeana-Sánchez (2009)

Discussiones Mathematicae Graph Theory

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Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there...

Kernels in monochromatic path digraphs

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

Discussiones Mathematicae Graph Theory

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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 ∈...

Monochromatic paths and monochromatic sets of arcs in bipartite tournaments

Hortensia Galeana-Sánchez, R. Rojas-Monroy, B. Zavala (2009)

Discussiones Mathematicae Graph Theory

Similarity:

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours and all of them are used. 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 for every pair of vertices there is no monochromatic path between them and for every vertex v in V(D)∖N there is a monochromatic path from v to some vertex in N. We denote by A⁺(u) the set of arcs of D that have u as...