Characterizations of graph classes via convex geometries: a survey

TL;DR

This survey reviews how convex geometries are used to characterize various graph classes, summarizing key results and providing new insights into their structural properties.

Contribution

It compiles existing characterizations of graph classes via convex geometries and offers new contributions to understanding these relationships.

Findings

Many graph classes can be characterized as convex geometries.

Convexity properties reveal structural insights into graph classes.

The survey highlights open problems and future research directions.

Abstract

Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey results on characterizations of well-known classes of graphs via convex geometries. We also give some contributions to this subject.