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Article
Classification of Minimal Separating Sets in Low Genus Surfaces
Mathematics and Statistics Faculty Publications and Presentations
  • J. J. P. Veerman, Portland State University
  • William Maxwell, Portland State University
  • Victor Rielly, Portland State University
  • Austin K. Williams, Portland State University
Document Type
Article
Publication Date
12-1-2017
Subjects
  • Combinatorial topology -- Data processing,
  • Topological graph theory,
  • Set theory
Abstract

Consider a surface S and let MS. If S \ M is not connected, then we say M separates S, and we refer to M as a separating set of S. If M separates S, and no proper subset of M separates S, then we say M is a minimal separating set of S. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus g = 2 and g = 3. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.

Persistent Identifier
https://pdxscholar.library.pdx.edu/mth_fac/210
Citation Information
Veerman, J. J. P., William J. Maxwell, Victor Rielly, and Austin K. Williams. "Classification of Minimal Separating Sets in Low Genus Surfaces." arXiv preprint arXiv:1701.04496 (2017).