Small Ramsey Numbers
By Stanislaw P. Radziszowski. 2011
604 citations recorded by the source corpus.
We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/43e849c505f50f2af90986ff5ab4f1c3169fa83a
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Highly connected monochromatic subgraphs of multicolored graphs (2009, neutral): “[5] or [16] for results and problems).”
- C-perfect hypergraphs (2010, background): “The quantity minG2M(H) n(G) is the classical Ramsey number r(H) of H. For a regularly updated survey on Ramsey numbers of all kinds of graphs, see [ 8 ].”
- Rainbow Generalizations of Ramsey Theory - A Dynamic Survey (2014, background): “The first is the dynamic survey [146] by Radziszowski which contains a wonderful list of known (monochromatic) Ramsey numbers.”
- Diagonal Ramsey via effective quasirandomness (2020, background): “See [5] for a comprehensive survey of Ramsey theory, and [15] for a dynamic survey of Ramsey theory for small numbers.”