Some properties of graph edge clique coverings

Edge clique coverings are investigated in graph theory for a long time. It is shown in some works that if the number of cliques in the minimal edge clique covering is fixed we can make estimation on some important graph characteristics. Also graph representation as a set of cliques can reduce the size of memory needed to keep the graph in it. Some important problems of edge clique coverings are investigated in the article including some properties of edge clique covering structure and construction of the minimal edge clique covering. There are investigated several features of graphs for which the task of finding the minimal edge clique covering can be divided into smaller parts which give less complexity in sum. Besides, the heuristic algorithm is proposed for constructing the edge clique covering of a graph.