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Disjoint homometric sets in graphs

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János Pach
2011
journal articles

Abstract

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) < h(n) < n/4, for n > 3.

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https://infoscience.epfl.ch/entities/publication/e1aa96cd-628d-42d0-b746-fdc1942ee8cf

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