Which directed graphs have a solution?
Mehdi Behzad, Frank Harary (1977)
Mathematica Slovaca
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Mehdi Behzad, Frank Harary (1977)
Mathematica Slovaca
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Hortensia Galeana-Śanchez, Rocío Sánchez-López (2016)
Discussiones Mathematicae Graph Theory
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For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no monochromatic directed path between them (N is mp-independent) and (2) for each vertex u in V (D) N there exists v ∈ N such that there is a monochromatic directed path from u to v in D (N is mp-absorbent). If every arc in D has a different...
Hortensia Galeana-Sánchez, V. Neumann-Lara (1998)
Mathematica Slovaca
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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...
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...
Peter Horák (1983)
Mathematica Slovaca
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H. Galeana-Sánchez, L. Pastrana Ramírez (1998)
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 set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the two following conditions (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and (ii) for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an...
H. Galeana-Sánchez, C. Hernández-Cruz (2014)
Discussiones Mathematicae Graph Theory
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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction...
Mieczysław Borowiecki, Danuta Michalak (1989)
Banach Center Publications
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Abas, M. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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