  Let $G=(V,E)$ be a finite connected graph along with a coloring of the
vertices of $G$ using the colors in a given set $X$. In this paper, we
introduce multi-color forcing, a generalization of zero-forcing on graphs, and
give conditions in which the multi-color forcing process terminates regardless
of the number of colors used. We give an upper bound on the number of steps
required to terminate a forcing procedure in terms of the number of vertices in
the graph on which the procedure is being applied. We then focus on multi-color
forcing with three colors and analyze the end states of certain families of
graphs, including complete graphs, complete bipartite graphs, and paths, based
on various initial colorings. We end with a few directions for future research.

Combinatorics