Absorbing sets in arc-coloured tournaments Original Research Article

Let T be a tournament whose arcs are coloured with k colours. Call a subset X of the vertices of T absorbing if from each vertex of T not in X there is a monochromatic directed path to some vertex in X. We consider the question of the minimum size of absorbing sets, extending known results and using new approaches. The greater part of the paper deals with finite tournaments, the last section treats infinite ones. In each case questions are suggested, both old and new.