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- W2086453403 abstract "We call the digraph D an orientation of a graph G if D is obtained from G by the orientation of each edge of G in exactly one of the two possible directions. The digraph D is an m -coloured digraph if the arcs of D are coloured with m -colours. Let D be an m -coloured digraph. 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 xy -monochromatic directed path. In this paper we obtain sufficient conditions for an m -coloured orientation of a graph obtained from K n by deletion of the arcs of K 1 , r ( 0 ⩽ r ⩽ n - 1 ) to have a kernel by monochromatic." @default.
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- W2086453403 date "2008-10-01" @default.
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- W2086453403 title "Kernels in edge-coloured orientations of nearly complete graphs" @default.
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- W2086453403 doi "https://doi.org/10.1016/j.disc.2007.08.079" @default.
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