Edge search number of cographs

We give a linear-time algorithm for computing the edge search number of cographs, thereby resolving the computational complexity of edge searching on this graph class. To achieve this we give a characterization of the edge search number of the join of two graphs. With our result, the knowledge on graph searching of cographs is now complete: node, mixed, and edge search numbers of cographs can all be computed efficiently. Furthermore, we are one step closer to computing the edge search number of permutation graphs.