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EMBEDDING DISTANCE GRAPHS IN FINITE FIELD VECTOR SPACES
Iosevich, Alex,Parshall, Hans Korean Mathematical Society 2019 대한수학회지 Vol.56 No.6
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 $d{\geq}2t$.
Embedding distance graphs in finite field vector spaces
Alex Iosevich,Hans Parshall 대한수학회 2019 대한수학회지 Vol.56 No.6
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 $A \subseteq \mathbf{F}_q^d$ 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 $d \geq 2t$.