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Abstract
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Many recent results in combinatorics concern the relationship between the size of a set and
the number of distances determined by pairs of points in the set. One extension of this
question considers configurations within the set with a specified pattern of distances.
In this paper, we use graph-theoretic methods to prove that a sufficiently large set
must contain at least
distinct copies of any
given weighted tree
, where
is a constant depending
only on the graph
.
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Keywords
finite point configurations, distance sets, graphs
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Mathematical Subject Classification 2010
Primary: 52C10
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Milestones
Received: 5 March 2018
Revised: 10 August 2018
Accepted: 8 September 2018
Published: 20 May 2019
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