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13.
Disjoint homometric sets in graphs
Albertson, Michael O. ; Pach, János ; Young, Michael E.
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 ▫$\frac{c \log n}{\log\log n} < h(n) < \frac{n}{4}$▫, for ▫$n > 3$▫.
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