Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647714 | Discrete Mathematics | 2013 | 6 Pages |
Abstract
We show that certain polyhedral versions of Sperner’s Lemma, where the colouring is given explicitly as part of the input, are PPAD-complete. The proofs are based on two recent results on the complexity of computational problems in game theory: the PPAD-completeness of 2-player Nash, proved by Chen and Deng, and of Scarf’s Lemma, proved by Kintali. We give a strengthening of the latter result, show how colourings of polyhedra provide a link between the two, and discuss a special case related to vertex covers.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Tamás Király, Júlia Pap,