2 research outputs found
Multilabeled versions of Sperner's and Fan's lemmas and applications
We propose a general technique related to the polytopal Sperner lemma for
proving old and new multilabeled versions of Sperner's lemma. A notable
application of this technique yields a cake-cutting theorem where the number of
players and the number of pieces can be independently chosen. We also prove
multilabeled versions of Fan's lemma, a combinatorial analogue of the
Borsuk-Ulam theorem, and exhibit applications to fair division and graph
coloring.Comment: 21 pages, 2 figure