A variant of the classical Ramsey problem

COMBINATORICA ◽  
1997 ◽  
Vol 17 (4) ◽  
pp. 459-467 ◽  
Author(s):  
Paul Erdős ◽  
András Gyárfás
Keyword(s):  
Ramsey Problem

scholarly journals On a Ramsey Problem Involving the 3-Pan Graph

2018 ◽  
Vol 16 (2) ◽  
pp. 437-441 ◽  
Author(s):  
Chula Jayawardene ◽  
Keyword(s):  
Ramsey Problem

scholarly journals Ramsey properties of randomly perturbed graphs: cliques and cycles

2020 ◽  
Vol 29 (6) ◽  
pp. 830-867 ◽  
Author(s):  
Shagnik Das ◽  
Andrew Treglown
Keyword(s):  
Random Graph ◽  
High Probability ◽  
Graph Model ◽  
Significant Progress ◽  
Random Choice ◽  
Ramsey Problem ◽  
Random Graph Model ◽  
Dense Graph ◽  
Precise Solution ◽  
Analogous Question

AbstractGiven graphs H1, H2, a graph G is (H1, H2) -Ramsey if, for every colouring of the edges of G with red and blue, there is a red copy of H1 or a blue copy of H2. In this paper we investigate Ramsey questions in the setting of randomly perturbed graphs. This is a random graph model introduced by Bohman, Frieze and Martin [8] in which one starts with a dense graph and then adds a given number of random edges to it. The study of Ramsey properties of randomly perturbed graphs was initiated by Krivelevich, Sudakov and Tetali [30] in 2006; they determined how many random edges must be added to a dense graph to ensure the resulting graph is with high probability (K3, Kt) -Ramsey (for t ≽ 3). They also raised the question of generalizing this result to pairs of graphs other than (K3, Kt). We make significant progress on this question, giving a precise solution in the case when H1 = Ks and H2 = Kt where s, t ≽ 5. Although we again show that one requires polynomially fewer edges than in the purely random graph, our result shows that the problem in this case is quite different to the (K3, Kt) -Ramsey question. Moreover, we give bounds for the corresponding (K4, Kt) -Ramsey question; together with a construction of Powierski [37] this resolves the (K4, K4) -Ramsey problem.We also give a precise solution to the analogous question in the case when both H1 = Cs and H2 = Ct are cycles. Additionally we consider the corresponding multicolour problem. Our final result gives another generalization of the Krivelevich, Sudakov and Tetali [30] result. Specifically, we determine how many random edges must be added to a dense graph to ensure the resulting graph is with high probability (Cs, Kt) -Ramsey (for odd s ≽ 5 and t ≽ 4).To prove our results we combine a mixture of approaches, employing the container method, the regularity method as well as dependent random choice, and apply robust extensions of recent asymmetric random Ramsey results.

scholarly journals An improved upper bound for the grid Ramsey problem

2020 ◽  
Vol 94 (4) ◽  
pp. 509-517
Author(s):  
Luka Milićević
Keyword(s):  
Upper Bound ◽  
Ramsey Problem

The Erdős–Hajnal hypergraph Ramsey problem

2020 ◽  
Vol 22 (4) ◽  
pp. 1247-1259 ◽  
Author(s):  
Dhruv Mubayi ◽  
Andrew Suk
Keyword(s):  
Ramsey Problem

scholarly journals A Ramsey problem of Harary on graphs with prescribed size

1987 ◽  
Vol 67 (3) ◽  
pp. 227-233 ◽  
Author(s):  
P Erdös ◽  
R.J Faudree ◽  
C.C Rousseau ◽  
R.H Schelp
Keyword(s):  
Ramsey Problem

scholarly journals On the Ramsey Problem for Multicolor Bipartite Graphs

1999 ◽  
Vol 22 (1) ◽  
pp. 48-59 ◽  
Author(s):  
W.A Carnielli ◽  
E.L Monte Carmelo
Keyword(s):  
Bipartite Graphs ◽  
Ramsey Problem

On a Quasi-Ramsey problem

1983 ◽  
Vol 7 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Paul Erdös ◽  
János Pach
Keyword(s):  
Ramsey Problem

OPTIMAL FISCAL POLICY WITH LAND FINANCING IN CHINA

2017 ◽  
Vol 23 (07) ◽  
pp. 2649-2674
Author(s):  
Shen Guo ◽  
Zheng Jiang
Keyword(s):  
Fiscal Policy ◽  
Value Added ◽  
Substantial Part ◽  
Welfare Gains ◽  
Ramsey Problem ◽  
Tax Rate ◽  
Special Instrument ◽  
Optimal Fiscal Policy ◽  
Conventional Instrument ◽  
The Government

This paper examines China's optimal fiscal policy in a general equilibrium model, in which the government finances its budget through both a special instrument, an implicit tax on the residential land, and a typical conventional instrument, the value-added tax (VAT). By solving a Ramsey problem, we find that (i) the optimal policy suggests a much lower land tax rate than the existing rate in China, and (ii) a substantial part of debt stabilization should come through an adjustment in the VAT rate, instead of relying on land financing. Switching from the existing policy to the Ramsey policy generates significant welfare gains.

scholarly journals A Euclidean Ramsey Problem

2003 ◽  
Vol 29 (2) ◽  
pp. 223-227 ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Ramsey Problem
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