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 .
"Embeddings of weighted graphs in Erdős-type settings." Mosc. J. Comb. Number Theory 8 (2) 117 - 123, 2019. https://doi.org/10.2140/moscow.2019.8.117