Improved bounds for embedding certain configurations in subsets of vector spaces over finite fields (Q6588170)

\textit{A. Iosevich} and \textit{H. Parshall} [J. Korean Math. Soc. 56, No. 6, 1515--1528 (2019; Zbl 1442.52013)] showed that for every \(E\subseteq \mathbb{F}_q^d\) \((d\geq2)\), and any connected graph \(G\) on \(k+1\) vertices with maximum degree \(m\), and any \(t\in \mathbb{F}_q\) with \(t\not= 0\), if \(|E|>Cq^{m+\frac{d-1}{2}}\), then there are \(k+1\) points in \(E\), such that the \(t\)-distance graph of these vertices is isomorphic to \(G\). The maximum degree in this result plays a bigger role than it deserves. The paper under review studies specific configurations of points to improve upon Iosevich and Parshall's results in certain cases.