Cover and partition problems of graphs are two central problems in graph theory. These problems have many applications in various domains. These domains include data mining or networks problems (clustering, community,..). The first problem is to cover optimally a graph by a set of vertices or edges or by a set of cycles or sub-graphs. The second problem is to cut optimally a graph in pieces following restrictions. Graph coloring is an example of partition problem which is subject to international active research. The objective of the Ph.D. is to study conjointly these two problems. The research will include coloring problems with restriction on colors, as in L(p,q)-coloring and [r,s,t]-coloring and with restriction on the neighborhood. Precisely, the packing coloring problem, a recently introduced problem, which is both a cover and a partition problem, is a major subject of the Ph.D.. Some results have been already established by members of the team. The applications of the studied problems include network aspects and data-mining.