Interval order representation via shortest paths
نویسنده
چکیده
Our goal in this paper is to illustrate how the representation theorems for finite interval orders and semiorders can be seen as special instances of existence results for potentials in digraphs. This viewpoint yields short proofs of the representation theorems and provides a framework for certain types of additional constraints on the intervals. We also use it to obtain a minimax theorem for the minimum number of endpoints in a representation. The techniques are based on techniques used by Peter Fishburn in proving results about bounded representations of interval orders.
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