An introduction to equitable DP coloring of graphs

A proper $k$-coloring of vertices of an $n$-vertex graph is equitable if the size of every color class is $\lfloor n\mathrm{/}k\rfloor$ or $\lceil n\mathrm{/}k\rceil$. An extension of it to list coloring requires only that the size of every color class is at most $\lceil n\mathrm{/}k\rceil$. 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.