Consistency in marked digraphs

In this paper we strive towards a mathematical theory for "marked digraphs" in which the nodes are signed. For completeness, we begin with an extensive list of definitions, including that of "consistency" in marked digraphs. We then provide three different descriptions of the concept: one an alternative in terms of directed cycles, another in terms of partitioning the nodes, and a third in terms of arc-digraphs and balance. We conclude with two additional observations, one characterizing the structure of consistent strongly connected marked tournaments and the other giving a criterion for a digraph to be "markable" in a consistent way.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22468/1/0000009.pd