Vol. 8, No. 2, 2019

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Embeddings of weighted graphs in Erdős-type settings

David M. Soukup

Vol. 8 (2019), No. 2, 117–123
Abstract

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 E must contain at least CG|E| distinct copies of any given weighted tree G, where CG is a constant depending only on the graph G.

Keywords
finite point configurations, distance sets, graphs
Mathematical Subject Classification 2010
Primary: 52C10
Milestones
Received: 5 March 2018
Revised: 10 August 2018
Accepted: 8 September 2018
Published: 20 May 2019
Authors
David M. Soukup
Department of Mathematics
UCLA
Los Angeles, CA
United States