Disjoint homometric sets in graphs
Michael O. Albertson, János Pach, Michael E. Young · Ars Mathematica Contemporanea · 2010
Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h ( n ) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h . It is shown that ( c log n )/(log log n ) 3.