Deciding Soccer Scores and Partial Orientations of Graphs
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We show that deciding if a simple graph has a partial ori- entation of its edges such that all vertices have a prescribed in-, out- and undirected degree, is NP-complete even for planar graphs. We prove that two related questions are also NP-complete, one is the decision of whether a score vector of a soccer-tournament is legal or not (we know who played who so far, but do not know the outcomes), the other is about a special edge-coloring of 3-uniform hypergraphs.
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