Connectedness of unit distance subgraphs induced by closed convex sets

HIGHLIGHTS

  • who: Remie Janssen and Leonie van Steijn from the (UNIVERSITY) have published the paper: Connectedness of Unit Distance Subgraphs Induced by Closed Convex Sets, in the Journal: (JOURNAL)
  • what: Instead of studying the chromatic number of these graphs, the authors investigate their connectedness and graph diameters. The authors aim to characterize when there is a path between any two points in a closed convex set using unit distance steps. The authors show that the authors can take P=x/λ. Now the authors show that there exists a Q ∈ X with d(x, Q) ≥ 1.
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