# Classification of Minimal Separating Sets in Low Genus Surfaces

## TL;DR

This paper classifies minimal separating sets in orientable surfaces of genus 2 and 3 using computational combinatorial topology, extending previous classifications for genus 0 and 1.

## Contribution

It provides a new classification of minimal separating sets for higher genus surfaces using computational methods, complementing earlier algebraic topology results.

## Key findings

- Classified minimal separating sets for genus 2 and 3 surfaces
- Extended the classification framework to higher genus surfaces
- Utilized computational combinatorial topology techniques

## Abstract

Consider a surface $S$ and let $M\subset S$. If $S\setminus M$ is not connected, then we say $M$ \emph{separates} $S$, and we refer to $M$ as a \emph{separating set} of $S$. If $M$ separates $S$, and no proper subset of $M$ separates $S$, then we say $M$ is a \emph{minimal separating set} of $S$. In this paper we use methods of computational 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.