New proofs of the uniqueness of extremal noneven digraphs.
Lim, Chjan C., Van Patten, Gregory K. (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Lim, Chjan C., Van Patten, Gregory K. (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Baskoro, E.T., Miller, M., Širáň, J. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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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...
Mehdi Behzad, Frank Harary (1977)
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...
Abas, M. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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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...
Halina Bielak, Elżbieta Soczewińska (1983)
Časopis pro pěstování matematiky
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Mieczysław Borowiecki, Danuta Michalak (1989)
Banach Center Publications
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