#### 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 ${C}_{G}|E|$ distinct copies of any given weighted tree $G$, where ${C}_{G}$ is a constant depending only on the graph $G$.

##### Keywords
finite point configurations, distance sets, graphs
Primary: 52C10