Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)

TL;DR

This survey reviews coloring, list coloring, and painting squares of graphs, emphasizing strong edge-coloring, with a focus on planar and sparse graph classes.

Contribution

It compiles and discusses recent research on coloring problems for squares of graphs, highlighting key results and open questions.

Findings

Focus on strong edge-coloring of graph squares

Emphasis on planar and sparse graphs

Summarizes recent advances and open problems

Abstract

We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.