I have a general (undirected) graph with a set of nodes, a set of edges, and a weight for each edge. I want to find a minimum clique cover of the vertices of the graph, that is, a partition of the graph into the smallest number of cliques. A clique is a set of nodes such that each pair of nodes is connected. I also want to maximize the sum of edge weights over the cliques. I want to use an integer programming approach for this problem.
Can any one give me some hints or some references that use mixed integer linear programming for the (maximum weight) minimum clique partition?
Thank you very much.
