Given a graph G = (V , E), a color set C(v) for each vertex v ∈ V , a bipartite graph between color sets C(u) and C(v) for every edge uv ∈ E, Conflict Coloring consists in deciding whether there exists a conflict coloring, that is a coloring in which c(u)c(v) is not an edge of the bipartite graph. Conflict Coloring is motivated by high-resolution determination of molecular assemblies. The graph represents the subunits and the interaction between them, the colors are the given conformations, and the edges of the bipartite graphs are the incompatible conformations of two subunits. In this paper, we first establish the complexity dichotomies (polynomial vs NP-complete) for Conflict Coloring and its variants. We provide some experiments in which we build instances of Conflict Coloring associated to Voronoi diagram in the plane, and we then analyse the existences of a solution related to parameters used in our experimental setup.