The Ramsey number of a graph with bounded maximum degree

  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},
Linear upper bounds for local Ramsey numbers
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
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
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
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 *
It is shown that for every positive integer d and each,0< <1, there exists kˆ k (d, ) such that forevery bipartite graph Gˆ (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
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
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
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


If G and H are graphs (which will mean finite, with no loops or parallel lines), define the Ramsey number r(G, H) to be the least number p such that if the lines of the complete graph Kp are colored
Regular Partitions of Graphs
Abstract : A crucial lemma in recent work of the author (showing that k-term arithmetic progression-free sets of integers must have density zero) stated (approximately) that any large bipartite graph
Regular partitions of graphs, in “Proc
  • Colloque Inter. CNRS”
  • 1978