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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55851", author = "Decha Samana and Vites Longani", title = "Lower Bounds of Some Small Ramsey Numbers", 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.", volume = "6", number = "9", pages = "1289-3", }