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http://dx.doi.org/10.4134/JKMS.j180776

EMBEDDING DISTANCE GRAPHS IN FINITE FIELD VECTOR SPACES  

Iosevich, Alex (Department of Mathematics University of Rochester)
Parshall, Hans (Department of Mathematics The Ohio State University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1515-1528 More about this Journal
Abstract
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.
Keywords
Erdos distance problem; finite fields; graph theory;
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Times Cited By KSCI : 1  (Citation Analysis)
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