Restricted subgraphs of edge-colored graphs and applications

TL;DR

This survey explores the theory and applications of rainbow subgraphs in edge-colored graphs, highlighting recent results and their relevance to various fields such as combinatorics, computer science, and coding theory.

Contribution

It provides a comprehensive overview of recent advances in the study of rainbow subgraphs and their applications across multiple disciplines.

Findings

Summarizes key results in rainbow subgraph existence

Demonstrates applications in graph decomposition and combinatorics

Connects theory to practical problems in computer science and coding

Abstract

A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding rainbow subgraphs or other restricted structures in edge-colored graphs has a long history, dating back to Euler's work on Latin squares. It has also proven to be a powerful method for studying several well-known questions in other areas. In this survey, we will provide a brief introduction to this topic, discuss several results in this area, and demonstrate their applications to problems in graph decomposition, additive combinatorics, theoretical computer science, and coding theory.