Lovasz' Conjecture and Other Applications of Topological Methods in Discrete Mathematics

TL;DR

This paper introduces topological methods and their applications in discrete mathematics, particularly in graph theory and combinatorics, highlighting their usefulness in proving theorems like Lovasz's conjecture.

Contribution

It provides an accessible introduction to topological concepts and showcases their applications in solving problems in discrete mathematics.

Findings

Topological methods can be effectively applied to discrete mathematics problems.

The paper illustrates applications to Lovasz's conjecture and related theorems.

Topological approaches offer new insights into combinatorial and graph theoretical problems.

Abstract

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as combinatorics, graph theory, and theoretical computer science. In this paper, we seek to provide an introduction to the relevant topological concepts to non-specialists, as well as a selection of some existing applications to theorems in discrete mathematics.