# Revisiting a theorem by Folkman on graph colouring

## TL;DR

This paper provides a concise proof of Folkman's 1969 theorem relating a graph's chromatic number to its subgraphs' properties, simplifying understanding of graph coloring bounds.

## Contribution

It offers a shorter, clearer proof of Folkman's theorem, enhancing theoretical understanding of graph coloring bounds.

## Key findings

- Proof simplifies Folkman's theorem understanding
- Establishes a new bound on chromatic number
- Clarifies relationship between graph parameters

## Abstract

We give a short proof of the following theorem due to Jon H. Folkman (1969): The chromatic number of any graph is at most $2$ plus the maximum over all subgraphs of the difference between half the number of vertices and the independence number.