Definitions and Basic Examples
In their by now classical paper Ramsey’s theorem for n-parameter sets Graham and Rothschild (1971) introduced the concept of parameter sets. The idea was to find a combinatorial abstraction of linear and affine vector spaces over finite fields. This was m
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Ramsey Theory for Discrete Structures
Ramsey Theory for Discrete Structures
Hans JRurgen PrRomel
Ramsey Theory for Discrete Structures
123
Hans JRurgen PrRomel Technische UniversitRat Darmstadt Darmstadt, Germany
ISBN 978-3-319-01314-5 ISBN 978-3-319-01315-2 (eBook) DOI 10.1007/978-3-319-01315-2 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013956012 Mathematics Subject Classification (2010): 05-02 © Springer International Publishing Switzerland 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
In spring 1986, I started as a PhD student at the Institute of Operations Research at the University of Bonn. At that time, Hans Jürgen Prömel was a PostDoc there and quickly became my mentor. Naturally, I was interested in his research and thus involved myself in proofreading large parts of his Habilitation thesis on Ramsey Theory for Discrete Structures. I still vividly remember that time: I had never been in touch with Ramsey theory before (and in fact never after), but I thoroughly enjoyed that exposure to a new area. The thesis was meant as a first part to a forthcoming monograph on Ramsey theory to be written jointly with Bernd Voigt. And with this in mind, the thesis was written. It was much more than a co
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