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}
}
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References

SHOWING 1-3 OF 3 REFERENCES
ON THE MAGNITUDE OF GENERALIZED RAMSEY NUMBERS FOR GRAPHS
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