Explicit Ramsey graphs and Erdos distance problem over finite Euclidean and non-Euclidean spaces
Combinatorics
2008-02-09 v1
Abstract
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).
Keywords
Cite
@article{arxiv.0711.3508,
title = {Explicit Ramsey graphs and Erdos distance problem over finite Euclidean and non-Euclidean spaces},
author = {Le Anh Vinh},
journal= {arXiv preprint arXiv:0711.3508},
year = {2008}
}