Displaying similar documents to “On (4, 2)-digraphs containing a cycle of length 2.”

k-Kernels and some operations in digraphs

Hortensia Galeana-Sanchez, Laura Pastrana (2009)

Discussiones Mathematicae Graph Theory

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Let D be a digraph. V(D) denotes the set of vertices of D; a set N ⊆ V(D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u,v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-directed path of length at most k-1. In this paper, we consider some operations on digraphs and prove the existence of k-kernels in digraphs formed...

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...

Degree sequences of digraphs with highly irregular property

Zofia Majcher, Jerzy Michael (1998)

Discussiones Mathematicae Graph Theory

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A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.

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...