# Computer-assisted graph theory: a survey

## TL;DR

This survey reviews a wide range of computer-assisted techniques in graph theory, highlighting their applications in various subfields and demonstrating new results enabled by computational methods.

## Contribution

It provides a comprehensive overview of computational approaches in graph theory, including novel applications and results across multiple subareas.

## Key findings

- Numerous detailed results in extremal graph theory and graph coloring.
- Demonstration of new results obtained through computer-assisted methods.
- Illustration of techniques like SAT solving and machine learning in graph theory.

## Abstract

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all pairwise non-isomorphic graphs within a given class, the use of searchable databases containing graphs and invariants as well as other established and emerging algorithmic paradigms. We cover approaches based on mixed integer linear programming, semidefinite programming, dynamic programming, SAT solving, metaheuristics and machine learning. The techniques are illustrated with numerous detailed results covering several important subareas of graph theory such as extremal graph theory, graph coloring, structural graph theory, spectral graph theory, regular graphs, topological graph theory, special sets in graphs, algebraic graph theory and chemical graph theory. We also present some smaller new results that demonstrate how readily a computer-assisted graph theory approach can be applied once the appropriate tools have been developed.