Abstract
We answer a variant of a question of Rödl and Voigt by showing that, for a given infinite cardinal λ, there is a graph G of cardinality κ = (2λ)+ such that for any colouring of the edges of G with λ colours, there is an induced copy of the κ-tree in G in the set theoretic sense with all edges having the same colour.
Dedicated to the memory of Eric Milner
Paper Sh 578 in Shelah’s publication list. Research supported by “The Israel Science Foundation” administered by The Israel Academy of Sciences and Humanities.
Research supported by NSERC grant #69–0982.
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References
P. Erdős and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956) 427–489.
A. Hajnal and P. Komjath, Embedding graphs into colored graphs, Trans. Amer. Math. Soc. 307 (1988), 395–409; Corrigendum: 332 (1992), 475.
P. Komjath and E.C. Milner, On a conjecture of Rödl and Voigt. J. Combin. Theory, Ser. B 61 (1994), 199–209.
V. Rödl and B. Voigt, Monochromatic trees with respect to edge partitions, J. Combin. Theory Ser. B 58 (1993), 291–298.
Saharon Shelah [Sh: 289], Consistency of positive partition theorems for graphs and models, in: Set theory and its applications (Toronto, ON, 1987), Lecture Notes in Mathematics 1401, (J. Steprans and S. Watson, eds.), Springer, Berlin-New York, (1989) 167–193.
Saharon Shelah [Sh: 365], There are Jonsson algebras in many inaccessible cardinals, in: Cardinal Arithmetic, Oxford Logic Guides 29 chapter III, Oxford University Press, 1994.
Saharon Shelah [Sh: 413], More Jonsson Algebras and Colourings, Archive for Mathematical Logic, to appear.
Saharon Shelah [Sh: 572], Colouring and ℵ2-cc not productive, Annals of Pure and Applied Logic, 84 (1997), 153–174.
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Shelah, S., Milner, E.C. (1998). A Tree-Arrowing Graph. In: Di Prisco, C.A., Larson, J.A., Bagaria, J., Mathias, A.R.D. (eds) Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8988-8_11
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DOI: https://doi.org/10.1007/978-94-015-8988-8_11
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