Explicit Ramsey graphs and Erdos distance problem over finite Euclidean and non-Euclidean spaces

Understand

We study the Erdos distance problem over finite Euclidean and non-Euclidean spaces.

• Our main tools are graphs associated to finite Euclidean and non-Euclidean spaces that are considered in Bannai-Shimabukuro-Tanaka (2004, 2007).
• These graphs are shown to be asymptotically Ramanujan graphs.
• The advantage of using these graphs is twofold.