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