Abstract
Let D denote a class of digraph such that every induced digraph in D is in D again. Then either D contains all acyclic digraphs or almost no graph has an orientation in D. Proofs and variations on this theme are discussed. Some open problems in Ramsey theory are raised.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Infinite and Finite Sets, Coll. Math. Soc. János Bolyai 10 (Keszthely 1973), Budapest 1976.
Combinatorics, Coll. Math. Soc. János Bolyai 18 (Keszthely 1976), North Holland Pub. Co., 1978.
V. Bienia, H. Meyniel, Séminaire du Lundi, MSH, Paris, 1984.
B. Bollobás, Geodesies in oriented graphs, Ann. Disc. Math. 20 (1984) 76–73.
W. Deuber, Generalizations of Ramsey’s theorem, in Infinite and Finite Sets, Coll. Math. Soc. János Bolyai 10 (Keszthely 1973), Budapest 1976 ([1]) 323–332.
P. Erdős, A. Hajnal, L. Pósa, Strong embeddings of graphs into colored graphs, in Infinite and Finite Sets, Coll. Math. Soc. János Bolyai 10 (Keszthely 1973), Budapest 1976. ([1]) 585–595.
R. L. Graham, B.L. Rothschild, Some recent developments in Ramsey theory: in Combinatorics, M. Hall Jr. and J.H. Van Lint eds., D. Reidel Publ. Co., Dordrecht-Boston 1975, 261–276.
J. Nešetřil, V. Rödl, Partition (Ramsey) Theory — A survey, in Combinatorics, Coll. Math. Soc. János Bolyai 18 (Keszthely 1976), North Holland Pub. Co., 1978. ([2]) 759–792.
J. Nešetřil, V. Rödl, Partitions of finite relational and set systems, J. Comb. Th. (A), 22 (1977) 289–312.
J. Nešetřil, V. Rödl, A simple proof of the Galvin-Ramsey property of the class of all finite graphs and a dimension of a graph, Disc. Math. 23 (1978) 49–55.
J. Nešetřil, V. Rödl, Extensions of full Ramsey theorem in the categories of all graphs and the categories of relations, Pamphlet 2, 1974 (mimeo Charles Univ., Praha).
J. Nešetřil, V. Röd1, On a probabilistic graph-theoretical method, Proc. Amer. Math. Soc. 72 (1978) 417–421.
J. Nešetřil, V. Rödl, Combinatorial partitions of finite posets and lattices — Ramsey lattices Alg. Univ. 19 (1984) 106–119.
V. Rödl, A generalization of Ramsey theorem, in: Graphs, Hypergraphs and Block Systems (Zielona Gora 1976) 211–220.
V. Rödl, Dimension of a graph and a generalization of Ramsey theorem (Czech), Thesis, Charles Univ., Praha (1973).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cochand, M., Duchet, P. (1989). A Few Remarks on Orientation of Graphs and Ramsey Theory. In: Halász, G., Sós, V.T. (eds) Irregularities of Partitions. Algorithms and Combinatorics 8, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61324-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-61324-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50582-2
Online ISBN: 978-3-642-61324-1
eBook Packages: Springer Book Archive