-panchromatic digraphs

Let and be two digraphs; without loops or multiple arcs. An coloring of is a function. We say that is an colored digraph. For an arc of, we say that is the color of over the coloring. A directed path in is an path if is a directed walk in. An kernel in an colored digraph is a subset of vertices of, say, such that for every pair of different vertices in there is no path between them and every vertex outside can reach by an path. A digraph is an -panchromatic digraph if has an kernel for every digraph and every coloring of. In this paper we show that -panchromatic digraphs cannot be characterized by means of certain forbidden subdigraphs. Also we will show -panchromaticity of some classes of digraphs and we show that -panchromaticity can be hereditary in some operations of digraphs.

Abstract licence: CC BY-NC

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