Minimum dominating cycles in outerplanar graphs

Adominating cycle of a graph lies at a distance of at most one from all the vertices of the graph. The problem of finding the minimum size of such a cycle is proved to be difficult even when restricted to planar graphs. An efficient algorithm solving this problem is given for the class of two-connectedouterplanar graphs, in which all vertices lie on the exterior face in a plane embedding of the graph.On leave from Institute of Computer Science, University of Wrocaw, Wrocaw, Poland.