A note on the p - center problem

The p - center problem is to locate p facilities in a network so as to minimize the longest distance between a demand point and its nearest facility. In this paper, we give a construction on a graph G which produces an infinite ascending chain G=G0≤G1≤G2≤... of graphs containing G such that given any optimal solution X for the p - center problem on G, X is an optimal solution for the p - center problem on i G for any i ≥ 1.