Horizons of Combinatorics
Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well. The recent volume contains high level surveys on these topics with auth
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BOLYAI SOCIETY MATHEMATICAL STUDIES Series Editor: Gabor Fejes T6th
Publication Board: Gyula O. H. Katona Laszl6 Lovasz Peter Pal PaIfy Andras Recski Andras Stipsicz Domokos Szasz
Managing Editor: Dezso Mikl6s 1. Combinatorics, Paul Erdos is Eighty,Vol. 1 D. Mikl6s) ~T. S6s) T. Sz(S nyi (Eds.) 2.. Combinatorics, Paul Erdδs is Eighty,Vol. 2. D. Mikl6s) V.’T.S6s) ’T. Sz(S nyi (Eds.) 3. Extremal Problems for Finite Sets P. Frankl) Z. Fiiredi) G. Katona) D. Mikl6s (Eds.) 4. Topology with Applications A. Csaszar (Ed.) S. Approximation Theory and Function Series P. Vertesi, L. Leindler, Sz. Revesz, J. Szabados, V. Totik (Eds.) 6. Intuitive Geometry I. Barany) K. Bδrδczky (Eds.) 7. Graph Theory and Combinatorial Biology L. Lovasz, A. Gyarfas , G. Katona, A. Recski (Eds.) 8. Low Dimensional Topology K.Boroczk 꺼 Jr. , W. Neumann)A. Stipsicz (Eds.) 9. Random Walks P. Revesz) B. T6th (Eds.) 10. Contemporary Combinatorics B. Bollobas (Ed.) 11. Paul Erdos and His Mathematics 1+11 G. Halasz) L. Lovasz) M. Simonovits,V. T. S6s (Eds.) 12.. Higher Dimensional Varieties and Rational Points K. Boroczky) Ir.) I. Kollar) ’T. Szamuely (Eds.) 13. Surgeryon Contact 3-Manifolds and Stein Surfaces B. Ozbagci) A. I. Stipsicz 14. A Panorama of Hungarian Mathematics in the ’IWentieth Century,VOI.1 I. Horvath (Ed.) IS. More Sets, Graphs and Numbers E. Gy6ri, G. Katona, L. Lovasz (Eds.) 16. Entropy, Search, Complexity I. Csiszar) G. Katona) G. Tardos (Eds.)
Ervin Gyori
Gyula O. H. Katona Lasz16 Lovasz (Eds.)
#환
K lIS JANOS BOLYAI MATHEMATICAL SOCIETY
Ervin Gy6ri
Managing Editor:
Hungarian Academy of Sciences Alfred Renyi Ins t. of Mathematics Realtanoda u. 13-15 Budapest 1053, Hungary e-mail: [email protected]
Gabor Sagi
Gyula
O. H. Katona
Hungarian Academy of Sciences Alfred Renyi Ins t. of Mathematics Realtanoda u. 13-15 Budapest 1053, Hungary e-mail: [email protected]
Hungarian Academy of Sciences Alfred Renyi Ins t. of Mathematics Realtanoda u. 13-15 Budapest 1053, Hungary e-mail: [email protected] Laszlo Lovasz Eotvos University Institute of Mathematics Pazmany Peter setany 11C Budapest 111기 Hungary e-mail: [email protected]
The publication of the recent volume was supported by the Hungarian Academy of Sciences.
Mathematics Subject Classification (2000): 03XX, 05XX, 52C10 , 6oC5 , 62XX
Library of Congress Control Number: 2007941335 ISSN 1217-4696 ISBN 3-540-77199-9 Springer Berlin Heidelberg New York ISBN 978-963-9453-09-8 Janos Bolyai Mathematical Society, Budapest This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations , recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version , and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German
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