论文信息 - Two notions of unit distance graphs

Two notions of unit distance graphs

A complete (unit) distance graph in ℝo(1))dn log2 n, while the number of distance graphs in ℝd on n labelled vertices is 2(1−1/⌊d/2⌋+o>(1))n 2/2. This is used to study a Ramsey type question involving these graphs. Finally, we discuss the following problem: what is the minimum number of edges a graph must have so that it is not realizable as a complete distance graph in ℝd?

Noga Alon | Andrey Kupavskii | N. Alon | A. Kupavskii

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