On maximal graphs with a k-clique

In this paper we present a novel approach towards constructing a maximal edge graph with a k-clique. The problem is NP-hard and we describe an efficient heuristic to arrive at an approximate solution. As the main contribution of this paper, we show that the above problem can be easily reduced to the problem of graph embedding with constraints. We also analyze the complexity of our method. This method finds application in many important fields of VLSI CAD, job scheduling and operations research