List coloring with requests

TL;DR

This paper investigates how to maximize the number of preferred vertex colors respected in list colorings of graphs, exploring various questions and suggesting future research directions.

Contribution

It introduces the problem of respecting vertex preferences in list coloring and explores multiple related questions, proposing new research directions.

Findings

Identified key questions in list coloring with preferences

Proposed methods to analyze preference-respecting colorings

Outlined future research avenues in the area

Abstract

Let G be a graph with a list assignment L. Suppose a preferred color is given for some of the vertices; how many of these preferences can be respected when L-coloring G? We explore several natural questions arising in this context, and propose directions for further research.