# Determining the finite subgraphs of curve graphs

## TL;DR

This paper presents an algorithmic method to identify whether a finite graph can be embedded as an induced subgraph within a curve graph, advancing understanding of the structure of curve graphs.

## Contribution

It introduces the first known algorithm to decide subgraph containment in curve graphs, providing a computational approach to a geometric graph theory problem.

## Key findings

- Algorithm exists for subgraph detection in curve graphs
- Decidability of induced subgraph problem established
- Advances understanding of curve graph structures

## Abstract

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.