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Mathematics > Combinatorics

arXiv:1801.02044 (math)
[Submitted on 6 Jan 2018 (v1), last revised 9 May 2019 (this version, v3)]

Title:Multilabeled versions of Sperner's and Fan's lemmas and applications

Authors:Frédéric Meunier, Francis Edward Su
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Abstract: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.
Comments: 21 pages, 2 figures
Subjects: Combinatorics (math.CO); Computer Science and Game Theory (cs.GT); Algebraic Topology (math.AT)
MSC classes: Primary 55M20, Secondary 54H25, 05E45, 91B32
Cite as: arXiv:1801.02044 [math.CO]
  (or arXiv:1801.02044v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1801.02044

Submission history

From: Francis Su [view email]
[v1] Sat, 6 Jan 2018 16:20:10 UTC (40 KB)
[v2] Mon, 5 Mar 2018 22:29:20 UTC (41 KB)
[v3] Thu, 9 May 2019 17:31:22 UTC (48 KB)
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