A survey of bounds for classical Ramsey numbers

DOI10.1002/jgt.3190070105zbMath0508.05046OpenAlexW2011896212MaRDI QIDQ4745846

Charles M. Grinstead, Fan R. K. Chung

Publication date: 1983

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.3190070105

zbMATH Keywords

Ramsey numbersRamsey functions

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Generalized Ramsey theory (05C55)

Related Items (22)

Some new computer generated results in Ramsey graph theory ⋮ Quantitative theorems for regular systems of equations ⋮ On Multicolor Ramsey Numbers and Subset Coloring of Hypergraphs ⋮ Lower bounds for bi-colored quaternary Ramsey numbers ⋮ A Fast Deterministic Detection of Small Pattern Graphs in Graphs Without Large Cliques ⋮ The Shannon capacity of a communication channel, graph Ramsey number and a conjecture of Erdős ⋮ Some properties of Ramsey numbers ⋮ Edge-colorings avoiding rainbow and monochromatic subgraphs ⋮ A fast deterministic detection of small pattern graphs in graphs without large cliques ⋮ A tutorial on the use of graph coloring for some problems in robotics ⋮ Regular languages viewed from a graph-theoretic perspective ⋮ Upper and lower Ramsey bounds in bounded arithmetic ⋮ Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory ⋮ An adaptive upper bound on the Ramsey numbers $R(3,\dots,3)$ ⋮ Lower bounds for small diagonal Ramsey numbers ⋮ On a diagonal conjecture for classical Ramsey numbers ⋮ A note on upper bounds for some Ramsey numbers ⋮ Edge-colored complete graphs with precisely colored subgraphs ⋮ Difference Ramsey numbers and Issai numbers ⋮ On Some Open Questions for Ramsey and Folkman Numbers ⋮ Three color Ramsey number of \(K_ 4-e\) ⋮ Quantitative forms of a theorem of Hilbert

Cites Work

• An upper bound on the Ramsey numbers R(3,k)
• On group partitions associated with lower bounds for symmetric Ramsey numbers
• Sum-free sets and Ramsey numbers. II
• Graph Theory and Probability. II
• New lower bounds of some diagonal Ramsey numbers
• Construction of Special Edge-Chromatic Graphs
• Backtrack Programming
• Combinatorial Relations and Chromatic Graphs

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