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The Vertex-Disjoint and Edge-Disjoint Ramsey Numbers of a Set of Graphs

Axioms
The Ramsey number R(F) of a graph F without isolated vertices is the smallest positive integer n such that every red–blue coloring of Kn produces a subgraph isomorphic to F all of whose edges are colored the same.
Emma Jent, Ping Zhang
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Planar Ramsey Numbers

Discussiones Mathematicae Graph Theory, 2005
Summary: The planar Ramsey number \(\text{PR}(G, H)\) is defined as the smallest integer \(n\) for which any 2-colouring of the edges of \(K_n\) with red and blue, where red edges induce a planar graph, leads to either a red copy of \(G\), or a blue copy of \(H\).
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New directions in Ramsey theory [PDF]

Discrete Mathematics Letters, 2021
Gary Chartrand, Ping Zhang
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Star-Critical Weakened Ramsey Numbers

Theory and Applications of Graphs
The weakened Ramsey number $r^{s,t}(G)$ is defined to be the least $p\in \mathbb{N}$ such that every $t$-coloring of the edges of the complete graph $K_p$ contains a subgraph isomorphic to $G$ that is spanned by edges that use at most $s$ colors ($1\le s\
Mark Budden, Monu Moun, Jagjeet Jakhar
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Optimization of Operation Parameters in a Cesium Atomic Fountain Clock Using Monte Carlo Method

IEEE Access, 2021
Number of detected atoms and contrast of Ramsey fringe are critical operation parameters in an atomic fountain clock. To optimize these operation parameters, a Monte Carlo method is utilized to simulate the evolution of the atomic cloud. It is found that
Hui Li, Yuanbo Du, Xian Yang, Yunyi Guo, Mingming Liu, Wenbing Li, Hongli Liu, Zehuang Lu   +7 more
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List Ramsey numbers

Journal of Graph Theory, 2020
AbstractWe introduce a list‐coloring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are far apart.
Noga Alon, Matija Bucic, Tom Kalvari, Eden Kuperwasser, Tibor Szabó   +4 more
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A note on the Ramsey numbers for theta graphs versus the wheel of order 5

AKCE International Journal of Graphs and Combinatorics, 2018
The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat, Mohammad S. Bataineh, Tomáš Vetrík, Ayat M.M. Rabaiah   +3 more
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Sidon–Ramsey and $$B_{h}$$-Ramsey numbers

Boletín de la Sociedad Matemática Mexicana
AbstractFor a given positive integer k, the Sidon–Ramsey number $${{\,\textrm{SR}\,}}(k)$$ SR ( k ) is defined as the minimum ...
Manuel A. Espinosa-García, Amanda Montejano, Edgardo Roldán-Pensado, J. David Suárez   +3 more
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Ramsey numbers for triples

Discrete Mathematics, 1975
AbstractSome recurrence inequalities for Ramsey numbers for triples are established by means of explicit constructions.
Harvey L. Abbott, Andrew Chiang-Fung Liu
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Anti-Ramsey numbers for disjoint copies of graphs [PDF]

Opuscula Mathematica, 2017
A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph \(G\) and a positive integer \(n\), the anti-Ramsey number \(ar(n,G)\) is the maximum number of colors in an edge-coloring of \(K_n\) with no ...
Izolda Gorgol, Agnieszka Görlich
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