Geodesic
Kernels in the closure of coloured digraphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 243-254

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Let D be a digraph with V(D) and A(D) the sets of vertices and arcs of D, respectively. A kernel of D is a set I ⊂ V(D) such that no arc of D joins two vertices of I and for each x ∈ V(D)∖I there is a vertex y ∈ I such that (x,y) ∈ A(D). A digraph is kernel-perfect if every non-empty induced subdigraph of D has a kernel. If D is edge coloured, we define the closure ξ(D) of D the multidigraph with V(ξ(D)) = V(D) and A(ξ(D)) = ⋃_i(u,v)with colour i there exists a monochromatic path of colour i from the vertex u to the vertex v contained in D.
Keywords: kernel, closure, tournament 
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     title = {Kernels in the closure of coloured digraphs},
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Galeana-Sánchez, Hortensia; García-Ruvalcaba, José. Kernels in the closure of coloured digraphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 243-254. http://geodesic.mathdoc.fr/item/DMGT_2000_20_2_a7/