Kernels, stable matchings, and Scarf's Lemma
نویسندگان
چکیده
Scarf's Lemma originally appeared as a tool to prove the non-emptiness of the core of certain NTU games. More recently, however, several applications have been found in the area of graph theory and discrete mathematics. In this paper we present and extend some of these applications. In particular, we prove results on the existence of kernels in orientations of h-perfect graphs. We describe a new direct link between Scarf's Lemma and Sperner's Lemma giving a new proof to the former.
منابع مشابه
Complexity of Scarf’s Lemma and Related Problems
Scarf’s lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N -person game. Over the last four decades, the usefulness of Scarf’s lemma has been demonstrated in several important combinatorial problems seeking stable solutions ([12], [1] [2], [15]). However, the complexity of the computational version of Scarf’s lemma (Scarf) remained open. In...
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تاریخ انتشار 2009