Classification of Minimal Separating Sets in Low Genus Surfaces

Authors

J. J. P. Veerman, Portland State UniversityFollow
William Maxwell, Portland State University
Victor Rielly, Portland State University
Austin K. Williams, Portland State University

Document Type

Article

Publication Date

12-2017

Subjects

Combinatorial topology -- Data processing, Topological graph theory, Set theory

Abstract

Consider a surface S and let M ⊂ S. 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://archives.pdx.edu/ds/psu/25783

Citation Details

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).