Blocking Sets for Paths of a Given Length

Paul Erdés1, Ralph Faudree2, Edward T. Ordman2, Cecil Rousseau2, Richard Schelp 2
1 Hungarian Academy of Sciences
2Department of Mathematical Sciences The University of Memphis Memphis, Tennessee 38152-3240

Abstract

How many vertices must we delete from a graph so that it no longer contains a path \(P_k\) on \(k\) vertices? We explore this question for various special graphs (hypercubes, square lattice graphs) as well as for some general families.