A time-optimal solution for the path cover problem on cographs

We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved time- and work-optimally for cographs. Our algorithm solves this problem in O(log n) time using n/log n processors on the EREW-PRAM for an n-vertex cograph G represented by its cotree.