Small Ramsey Numbers

2011/08/22 by Stanisław Radziszowski · 3 citations
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Advanced Topology and Set Theory #Ramsey's theorem #Mathematics #Hypergraph #Combinatorics #Graph #Discrete mathematics #Enhanced Data Rates for GSM Evolution #Ramsey theory #Computer science

paper · doi:10.37236/21

openalex publication_date 2011/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• House of Graphs: A database of interesting graphs
• Subgraph Counting Identities and Ramsey Numbers
• On a Problem of Formal Logic
• The Ramsey number R(3, t) has order of magnitude t2/log t
• Ramsey numbers for cycles in graphs
• On the combinatorial problems which I would most like to see solved
• Combinatorial Relations and Chromatic Graphs
• On independent sets in hypergraphs
• Ramsey numbers of 3-uniform loose paths and loose cycles

Cited by

• Subgraph Counting Identities and Ramsey Numbers
• New Lower Bounds for 28 Classical Ramsey Numbers
• RAMSEY FOR COMPLETE GRAPHS WITH DROPPED CLIQUES
• Ramsey's theorem [wikipedia]