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- W1978984844 abstract "Let D be a finite digraph, V(D) and A(D) will denote the sets of vertices and arcs of D respectively. A kernel N of D is an independent set of vertices such that for every w∈V(D)−N there exists an arc from w to N. Let F be a set of arcs of D (i.e. F⊆A(D)), a set S⊆V(D) is called a semikernel of D modulo F if S is an independent set of vertices such that for every z∈V(D)−S for which there exists an Sz-arc of D−F, there also exists a zS-arc in D. In this paper is introduced the concept of semikernel modulo F and it is used to obtain a new sufficient condition for the existence of kernels in digraphs. As a consequence is obtained a generalization of the following result of B. Sands, N. Sauer and R. Woodrow; in case that the digraph is a finite digraph: Let D be a digraph whose arcs are coloured with two colors. If D contains no monochromatic infinite outward path, then there exists a set S of vertices of D such that: No two vertices of S are connected by a monochromatic directed path and for every vertex not in S there is a monochromatic directed path from x to a vertex in S." @default.
- W1978984844 created "2016-06-24" @default.
- W1978984844 creator A5029325738 @default.
- W1978984844 date "2000-05-01" @default.
- W1978984844 modified "2023-10-18" @default.
- W1978984844 title "Semikernels modulo F and kernels in digraphs" @default.
- W1978984844 doi "https://doi.org/10.1016/s0012-365x(99)00336-2" @default.
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