Computation of the biclique partition number for graphs with specific blocks

The biclique partition number of an undirected graph $G=(V,E)$ is the smallest number of bicliques (complete bipartite subgraphs) of the graph $G$ needed to partition the edge set $E.$ We present an efficient algorithm for finding the biclique partition number of a connected graph whose blocks are either complete graphs or complete bipartite graphs or cycles.