ON COVERING THE POINTS OF A GRAPH WITH POINT DISJOINT PATHS.

Abstract

The minimum number of point disjoint paths which cover all the points of a graph defines a covering number denoted by zeta . The relation of zeta to some other well-known graphical invariants is discussed, and zeta is evaluated for a variety of special classes of graphs. A simple algorithm is developed for determining zeta in the case of a tree, and it is shown that this tree algorithm can be generalized to yield zeta for any connected graph. Degree conditions are also derived which yield simple upper bounds for zeta .