Skip to main content
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
Publication Date
  • Combinatorial topology -- Data processing,
  • Topological graph theory,
  • Set theory

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
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).