On Hallian digraphs and their binding number
Mieczysław Borowiecki, Danuta Michalak (1989)
Banach Center Publications
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Mieczysław Borowiecki, Danuta Michalak (1989)
Banach Center Publications
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Mehdi Behzad, Frank Harary (1977)
Mathematica Slovaca
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Abas, M. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Peter Horák (1983)
Mathematica Slovaca
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Hortensia Galeana-Sánchez, José de Jesús García-Ruvalcaba (2001)
Discussiones Mathematicae Graph Theory
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A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V( ζ(D)) = V(D), and A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic...
Zdzisław Skupień (1999)
Discussiones Mathematicae Graph Theory
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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...
Miroslaw Arczyński, Mieczysław Borowiecki, Maciej M. Sysło (1979)
Colloquium Mathematicae
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Matúš Harminc, Roman Soták (1999)
Discussiones Mathematicae Graph Theory
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For given nonnegative integers k,s an upper bound on the minimum number of vertices of a strongly connected digraph with exactly k kernels and s solutions is presented.
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...