Digraphs of bounded elimination width

Hunter and Kreutzer recently introduced the digraph width measure Kelly-width. The measure is based on a vertex elimination process that aims at bounding the out-degree of a vertex during the elimination. We refine the Kelly-width measure by bounding both the out-degree and the in-degree of a vertex. We show that the elimination process and a subgraph characterisation of Kelly-width naturally generalise to the refined notion. The main result of the paper is a game characterisation of the refined measure, which is a surprisingly non-trivial generalisation of the game for Kelly-width.