Lower Bounds of Some Small Ramsey Numbers

Authors: Decha Samana, Vites Longani

Abstract:

For positive integer s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. We construct the circulant graphs and use them to obtain lower bounds of some small Ramsey numbers.

Keywords: Lower bound, Ramsey numbers, Graphs, Distance line.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332574

References:

[1] S.P.Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey 1, revision12, August 2009, http://www.combinatorics.org.
[2] G. Chartrand and L. Lesniak, Graph&Digraphs, 4th Edition, Chapman&Hall, 1996.
[3] D. Samana, V. Longani, Lower Bounds of Ramsey Numbers R(s, t), IAENG International Journal of Applied Mathematics, Volume 39, Issue 4, November(2009), http://www.iaeng.org/IJAM.