  We introduce a variant of the graph coloring problem, which we denote as {\sc
Budgeted Coloring Problem} (\bcp). Given a graph $G$, an integer $c$ and an
ordered list of integers $\{b_1, b_2, \ldots, b_c\}$, \bcp asks whether there
exists a proper coloring of $G$ where the $i$-th color is used to color at most
$b_i$ many vertices. This problem generalizes two well-studied graph coloring
problems, {\sc Bounded Coloring Problem} (\bocp) and {\sc Equitable Coloring
Problem} (\ecp) and as in the case of other coloring problems, it is \nph even
for constant values of $c$. So we study \bcp under the paradigm of
parameterized complexity. \begin{itemize}
  \item We show that \bcp is \fpt (fixed-parameter tractable) parameterized by
the vertex cover size. This generalizes a similar result for \ecp and
immediately extends to the \bocp, which was earlier not known.
  \item We show that \bcp is polynomial time solvable for cluster graphs
generalizing a similar result for \ecp. However, we show that \bcp is \fpt, but
unlikely to have polynomial kernel, when parameterized by the deletion distance
to clique, contrasting the linear kernel for \ecp for the same parameter.
  \item While the \bocp is known to be polynomial time solvable on split
graphs, we show that \bcp is \nph on split graphs. As \bocp is hard on
bipartite graphs when $c>3$, the result follows for \bcp as well. We provide a
dichotomy result by showing that \bcp is polynomial time solvable on bipartite
graphs when $c=2$. We also show that \bcp is \nph on co-cluster graphs,
contrasting the polynomial time algorithm for \ecp and \bocp. \end{itemize}
Finally we present an $\mathcal{O}^*(2^{|V(G)|})$ algorithm for the \bcp,
generalizing the known algorithm with a similar bound for the standard
chromatic number.
