Abstract
This is an expository paper which surveys results related to the recent confirmation of the zero-sum-tree conjecture by Z. Füredi and D. Kleitman. The author believes that trees play a major role in zero-sum Ramsey theory. He makes some observations that may lead in the far future to very general theorems and presents a collection of fifteen conjectures attributed to various people. Some of the conjectures have already appeared in print but most of them are new.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Alon, P. Frankl and L. Lovász, The chromatic number of Kneser hypergraphs, Trans. Amer. Math. Soc 298 (1986) 359–370.
A. Bialostocki, Some combinatorial number theory aspects of Ramsey theory, research proposal (1989).
A. Bialostocki, Y. Caro, and Y. Roditty, On zero sum Turán numbers, Ars Combinatoria, 29A (1990) 117–127.
A. Bialostocki and P. Dierker, Zero sum Ramsey theorems, Congressus Numerantium 70 (1990) 119–130.
A. Bialostocki and P. Dierker, On zero sum Ramsey numbers: multiple copies of a graph, to appear in J. Graph Theory.
A. Bialostocki and P. Dierker, On the Erdős-Ginzburg-Ziv Theorem and the Ramsey numbers for stars and matchings, to appear in Discrete Math.
A. Bialostocki and P. Dierker, On zero sum Ramsey numbers: small graphs, Ars Combinatoria 29A (1990) 193–198.
A. Bialostocki and P. Dierker, Monochromatic connected subgraphs in a multicoloring of the complete graph, manuscript.
A. Bialostocki and M. Lotspeich, Some developments of the Erdős-Ginzburg-Ziv Theorem I, manuscript submitted.
S.A. Burr, P. Erdős, and J.H. Spencer, Ramsey theorems for multiple copies of graphs, Trans. Amer. Math. Soc. 209 (1975) 87–99.
J. Bierbauer and A. Gyárfás, On (n, k) colorings of complete graphs, Congressus Numerantium 58 (1987) 123–139.
Y. Caro, On zero-sum Ramsey numbers -stars, to appear in Discrete Math.
Y. Caro, On zero-sum Turán numbers -stars and cycles, to appear in Ars Combinatoria.
P. Erdős, A. Ginzburg and A. Ziv, Theorem in additive number theory, Bull. Research Council Israel 10F (1961) 41–43.
Z. Füredi and D.J. Kleitman, On zero-trees, to appear in J. Graph Theory.
R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory, John Wiley & Sons, New York-Chichester-Brisbane-Toronto, 1980.
J.E. Olson, On a combinatorial problem of Erdős, Ginzburg and Ziv, J. Number Theory 8 (1976) 52–57.
A. Schrijver and P.D. Seymour, A simpler proof and a generalization of the zero-trees theorem, to appear in J. Combinatorial Theory, Series A.
A. Schrijver and P.D. Seymour, Spanning trees of different weights, in “Polyhedral Combinatorics”, in DIMACS Series in Discrete Math. and Theoret. Comp. Sc. 1 (1990) (eds. W. Cook and P.D. Seymour).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bialostocki, A. (1993). Zero Sum Trees: A Survey of Results and Open Problems. In: Sauer, N.W., Woodrow, R.E., Sands, B. (eds) Finite and Infinite Combinatorics in Sets and Logic. NATO ASI Series, vol 411. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2080-7_2
Download citation
DOI: https://doi.org/10.1007/978-94-011-2080-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4923-8
Online ISBN: 978-94-011-2080-7
eBook Packages: Springer Book Archive