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Home / Journal of Computational and Theoretical Nanoscience, Volume 9, Number 10

An Algorithm for Finding Optimal Lower Bounds on Ramsey Numbers Based on Cyclic Graphs

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For integers s, t ≥ 1, the Ramsey number R(s, t) (resp. R(s, t)) is defined to be the least positive integer n such that every graph on n vertices contains either a Ks or its complement contains a Kt (resp. Kt – e). Ramsey number is one of the branches of Ramsey theory, which has many applications in information theory and theoretical computer science. In this paper, an algorithm is proposed to search lower bounds up to 121 from cyclic graphs for Ramsey numbers of type R(3, k), and some new low bounds for Ramsey numbers are obtained.

Keywords: CYCLIC GRAPH; EXHAUSTIVE SEARCH; GRAPH COLORING; RAMSEY NUMBER

Document Type: Research Article

Publication date: 01 October 2012

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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