Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EMBEDDING DISTANCE GRAPHS IN FINITE FIELD VECTOR SPACES

  • Received : 2018.11.16
  • Accepted : 2019.03.04
  • Published : 2019.11.01
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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 $d{\geq}2t$.

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References

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