# Combinatorics with Emphasis on the Theory of Graphs

• Jack E. Graver
• Mark E. Watkins
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 54)

1. Front Matter
Pages i-xv
2. Jack E. Graver, Mark E. Watkins
Pages 1-27
3. Jack E. Graver, Mark E. Watkins
Pages 28-56
4. Jack E. Graver, Mark E. Watkins
Pages 57-97
5. Jack E. Graver, Mark E. Watkins
Pages 98-125
6. Jack E. Graver, Mark E. Watkins
Pages 126-152
7. Jack E. Graver, Mark E. Watkins
Pages 153-177
8. Jack E. Graver, Mark E. Watkins
Pages 178-212
9. Jack E. Graver, Mark E. Watkins
Pages 213-229
10. Jack E. Graver, Mark E. Watkins
Pages 230-264
11. Jack E. Graver, Mark E. Watkins
Pages 265-309
12. Jack E. Graver, Mark E. Watkins
Pages 310-335
13. Back Matter
Pages 337-351

### Introduction

Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of unformulated or unrecognized general theorems. The body of knowledge has now reached a stage where approaches toward unification are overdue. To paraphrase Professor Gian-Carlo Rota (Toronto, 1967), "Combinatorics needs fewer theorems and more theory. " In this book we are doing two things at the same time: A. We are presenting a unified treatment of much of combinatorics and graph theory. We have constructed a concise algebraically­ based, but otherwise self-contained theory, which at one time embraces the basic theorems that one normally wishes to prove while giving a common terminology and framework for the develop­ ment of further more specialized results. B. We are writing a textbook whereby a student of mathematics or a mathematician with another specialty can learn combinatorics and graph theory. We want this learning to be done in a much more unified way than has generally been possible from the existing literature. Our most difficult problem in the course of writing this book has been to keep A and B in balance. On the one hand, this book would be useless as a textbook if certain intuitively appealing, classical combinatorial results were either overlooked or were treated only at a level of abstraction rendering them beyond all recognition.

### Keywords

Graph Kombinatorik algebra mathematics theorem

#### Authors and affiliations

• Jack E. Graver
• 1
• Mark E. Watkins
• 1
1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-9914-1
• Copyright Information Springer-Verlag New York 1977
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-9916-5
• Online ISBN 978-1-4612-9914-1
• Series Print ISSN 0072-5285
• Buy this book on publisher's site