Adjoint functors in graph theory

TL;DR

This paper surveys the application of adjoint functors in graph theory, highlighting their role in various topics like colourings, complexity, and duality, and unifying these concepts through categorical methods.

Contribution

It introduces a unified perspective on graph theory applications using adjoint functors, connecting diverse topics and raising new research questions.

Findings

Unifies graph theory concepts via adjoint functors.

Highlights adjoint functors' role in graph colourings and complexity.

Raises new questions in the application of categorical methods.

Abstract

We survey some uses of adjoint functors in graph theory pertaining to colourings, complexity reductions, multiplicativity, circular colourings and tree duality. The exposition of these applications through adjoint functors unifies the presentation to some extent, and also raises interesting questions.