gcp -- model for minimizing the number of colors in a graph
    Parameters:
        - V: set/list of nodes in the graph
        - E: set/list of edges in the graph
        - K: upper bound on the number of colors
    Returns a model, ready to be solved.

def gcp(V,E,K):
    """gcp -- model for minimizing the number of colors in a graph
    Parameters:
        - V: set/list of nodes in the graph
        - E: set/list of edges in the graph
        - K: upper bound on the number of colors
    Returns a model, ready to be solved.
    """
    model = Model("gcp")
    x,y = {},{}
    for k in range(K):
        y[k] = model.addVar(vtype="B", name="y(%s)"%k)
        for i in V:
            x[i,k] = model.addVar(vtype="B", name="x(%s,%s)"%(i,k))

    for i in V:
        model.addCons(quicksum(x[i,k] for k in range(K)) == 1, "AssignColor(%s)"%i)

    for (i,j) in E:
        for k in range(K):
            model.addCons(x[i,k] + x[j,k] <= y[k], "NotSameColor(%s,%s,%s)"%(i,j,k))

    model.setObjective(quicksum(y[k] for k in range(K)), "minimize")

    model.data = x
    return model