# The Ramsey number of a graph with bounded maximum degree

@article{Chvatl1983TheRN, title={The Ramsey number of a graph with bounded maximum degree}, author={C. Chvat{\'a}l and Vojtech R{\"o}dl and Endre Szemer{\'e}di and William T. Trotter}, journal={J. Comb. Theory, Ser. B}, year={1983}, volume={34}, pages={239-243} }

## 169 Citations

Linear upper bounds for local Ramsey numbers

- MathematicsGraphs Comb.
- 1987

The following conjecture of Gyárfás et al. is proved here: for each positive integerk there exists a constantc = c(k) such that rlock(G) ≤ crk(G), for every connected grraphG (whererk( G) is theusual Ramsey number fork colors).

Induced Ramsey Numbers

- MathematicsComb.
- 1998

The induced Ramsey number of pairs of graphs (G, H) is investigated to be the smallest possible order of a graph Γ with the property that, whenever its edges are coloured red and blue, either a red induced copy of G arises or else a blue induced copies of H arises.

On Ramsey Numbers of Sparse Graphs

- MathematicsCombinatorics, Probability and Computing
- 2003

It is shown that, for every , sufficiently large n, and any graph H of order , either H or its complement contains a (d,n)-common graph, that is, a graph in which every set of d vertices has at least n common neighbours.

Planar Graph Coloring with an Uncooperative Partner

- MathematicsPlanar Graphs
- 1991

It is shown that the game chromatic number of a planar graph is at most 33 and the concept of p-arrangeability, which was first introduced by Guantao and Schelp in a Ramsey theoretic setting, is bounded in terms of its genus.

On graphs with small Ramsey numbers *

- MathematicsJ. Graph Theory
- 2001

It is shown that for every positive integer d and each,0< <1, there exists k k (d, ) such that forevery bipartite graph G (W,U;E ) with the maximum degree of vertices in W at most d and jU j j jW j, R (G ) k jWJ.

On the Ramsey Number of Sparse 3-Graphs

- MathematicsGraphs Comb.
- 2008

This work considers a hypergraph generalization of a conjecture of Burr and Erdős concerning the Ramsey number of graphs with bounded degree and derives the analogous result for 3-uniform hypergraphs.

Size Ramsey numbers of triangle-free graphs with bounded degree

- Mathematics
- 2016

The size Ramsey number r̂(H) of a graph H is the smallest number of edges in a graph G which is Ramsey with respect to H, that is, such that every two-colouring of the edges of G contains a…

Tiling with monochromatic bipartite graphs of bounded maximum degree

- Mathematics
- 2021

We prove that for any r ∈ N, there exists a constant Cr such that the following is true. Let F = {F1, F2, . . . } be an infinite sequence of bipartite graphs such that |V (Fi)| = i and ∆(Fi) ≤ ∆ hold…

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