# Extremal Combinatorics

## With Applications in Computer Science

• Stasys Jukna
Book

1. Front Matter
Pages I-XVII
2. ### Prolog: What This Book Is About

1. Stasys Jukna
Pages 1-4
3. ### Notation

1. Stasys Jukna
Pages 5-8
4. ### The Classics

1. Front Matter
Pages 9-9
2. Stasys Jukna
Pages 11-22
3. Stasys Jukna
Pages 23-31
4. Stasys Jukna
Pages 32-36
5. Stasys Jukna
Pages 37-54
6. Stasys Jukna
Pages 55-64
7. Stasys Jukna
Pages 65-76
5. ### Extremal Set Theory

1. Front Matter
Pages 77-77
2. Stasys Jukna
Pages 79-88
3. Stasys Jukna
Pages 89-96
4. Stasys Jukna
Pages 97-108
5. Stasys Jukna
Pages 109-132
6. Stasys Jukna
Pages 133-142
7. Stasys Jukna
Pages 143-152
8. Stasys Jukna
Pages 153-166
6. ### The Linear Algebra Method

1. Front Matter
Pages 167-167
2. Stasys Jukna
Pages 169-190

### Introduction

Combinatorial mathematics has been pursued since time immemorial, and at a reasonable scientific level at least since Leonhard Euler (1707-1783). It ren­ dered many services to both pure and applied mathematics. Then along came the prince of computer science with its many mathematical problems and needs - and it was combinatorics that best fitted the glass slipper held out. Moreover, it has been gradually more and more realized that combinatorics has all sorts of deep connections with "mainstream areas" of mathematics, such as algebra, geometry and probability. This is why combinatorics is now apart of the standard mathematics and computer science curriculum. This book is as an introduction to extremal combinatorics - a field of com­ binatorial mathematics which has undergone aperiod of spectacular growth in recent decades. The word "extremal" comes from the nature of problems this field deals with: if a collection of finite objects (numbers, graphs, vectors, sets, etc. ) satisfies certain restrictions, how large or how small can it be? For example, how many people can we invite to a party where among each three people there are two who know each other and two who don't know each other? An easy Ramsey-type argument shows that at most five persons can attend such a party. Or, suppose we are given a finite set of nonzero integers, and are asked to mark an as large as possible subset of them under the restriction that the sum of any two marked integers cannot be marked.

### Keywords

Diskrete Mathematik Kombinatorik algorithms combinatorics computational complexity discrete mathematics extremal combinatorics extremal set theory linear algebra

#### Authors and affiliations

• Stasys Jukna
• 1
• 2
1. 1.Informatik - FB 20, Theoretische InformatikJohann Wolfgang Goethe-UniversitätFrankfurtGermany
2. 2.Institute of Mathematics and InformaticsVilniusLethuania

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-04650-0
• Copyright Information Springer-Verlag Berlin Heidelberg 2001
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-08559-8
• Online ISBN 978-3-662-04650-0
• Series Print ISSN 1862-4499