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

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

2007-11-22

arxiv.org/abs/0711.3508v1

The Electronics Journal of Combinatorics, 15 (2008), R5

Mathematics

Combinatorics

Scientific paper

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. First, we can derive new lower bounds on the Erdos distance problems with explicit constants. Second, we can construct many explicit tough Ramsey graphs R(3,k).

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