scholarly journals On Ramsey theory and graphical parameters

1977 ◽  
Vol 68 (1) ◽  
pp. 105-114 ◽  
Author(s):  
Linda Lesniak ◽  
John Roberts
Keyword(s):  
Ramsey Theory

scholarly journals Recent results in partition (Ramsey) theory for finite lattices

1981 ◽  
Vol 35 (1-3) ◽  
pp. 185-198 ◽  
Author(s):  
Hans Jürgen Prömel ◽  
Bernd Voigt
Keyword(s):  
Ramsey Theory ◽  
Finite Lattices

scholarly journals Abstract topological Ramsey theory for nets

2016 ◽  
Vol 201 ◽  
pp. 314-329 ◽  
Author(s):  
Vassiliki Farmaki ◽  
Dimitris Karageorgos ◽  
Andreas Koutsogiannis ◽  
Andreas Mitropoulos
Keyword(s):  
Ramsey Theory

Fundamentals of Ramsey Theory

2021 ◽  
Author(s):  
Aaron Robertson
Keyword(s):  
Ramsey Theory

Idempotents in compact semigroups and Ramsey theory

1989 ◽  
Vol 68 (3) ◽  
pp. 257-270 ◽  
Author(s):  
H. Furstenberg ◽  
Y. Katznelson
Keyword(s):  
Ramsey Theory ◽  
Compact Semigroups

scholarly journals Ordered Ramsey theory and track representations of graphs

2015 ◽  
Vol 6 (4) ◽  
pp. 445-456 ◽  
Author(s):  
Kevin G. Milans ◽  
Derrick Stolee ◽  
Douglas B. West
Keyword(s):  
Ramsey Theory

scholarly journals On Ramsey-Minimal Infinite Graphs

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Jordan Barrett ◽  
Valentino Vito
Keyword(s):  
Ramsey Theory ◽  
Infinite Graphs ◽  
Minimal Graph ◽  
Finite Graphs ◽  
Minimal Graphs ◽  
Finite Case ◽  
Ramsey Minimal Graph ◽  
General Conditions

For fixed finite graphs $G$, $H$, a common problem in Ramsey theory is to study graphs $F$ such that $F \to (G,H)$, i.e. every red-blue coloring of the edges of $F$ produces either a red $G$ or a blue $H$. We generalize this study to infinite graphs $G$, $H$; in particular, we want to determine if there is a minimal such $F$. This problem has strong connections to the study of self-embeddable graphs: infinite graphs which properly contain a copy of themselves. We prove some compactness results relating this problem to the finite case, then give some general conditions for a pair $(G,H)$ to have a Ramsey-minimal graph. We use these to prove, for example, that if $G=S_\infty$ is an infinite star and $H=nK_2$, $n \geqslant 1$ is a matching, then the pair $(S_\infty,nK_2)$ admits no Ramsey-minimal graphs.

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