An introduction to equitable DP coloring of graphs

TL;DR

This paper introduces equitable DP coloring, a generalization of equitable coloring, and explores its properties and potential applications in graph theory.

Contribution

It extends equitable coloring to the broader framework of DP coloring, providing new insights and properties of this generalized parameter.

Findings

Defined equitable DP coloring and its parameters

Analyzed properties and bounds of equitable DP coloring

Discussed potential applications in graph theory

Abstract

A proper $k$-coloring of vertices of an $n$-vertex graph is equitable if the size of every color class is $\lfloor n/k\rfloor$ or $\lceil n/k\rceil$. An extension of it to list coloring requires only that the size of every color class is at most $\lceil n/k\rceil$. Such colorings have interesting applications and have been actively studied recently. In this paper, we extend the notion of equitable coloring to the more general notion of equitable DP coloring and study properties of the new parameter.