Alternating kernels.

An arc-coloured digraph D is alternating if whenever ( u , v ) and ( v , w ) are arcs in D they are of different colours. In an arc coloured digraph D , a subset K ⊂ V ( D ) of vertices of D is a kernel by alternating paths (or alternating kernel ) if it is absorbent and independent by directed alternating paths. In this paper we prove sufficient conditions for the existence of alternating kernels in arc-coloured tournaments, quasi-transitive digraphs, and k -partite digraphs. [ABSTRACT FROM AUTHOR]