A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

Extremal Graph Theory

Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

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Graph Coloring Problems

From the Book:
PREFACE: When the first edition of this book was published in 1989, viruses and other forms of malicious code were fairly uncommon, the Internet was used largely by just computing professionals, a Clipper was a sailing ship, and computer crime was seldom a headline topic in daily newspapers. In that era most people were unconcerned about--even unaware of--how serious is the threat to security in the use of computers. 

The use of computers has spread at a rate completely unexpected back then. Now you can bank by computer, order and pay for merchandise, and even commit to contracts by computer. And the uses of computers in business have similarly increased both in volume and in richness. Alas, the security threats to computing have also increased significantly. 

Why Read This Book?

Are your data and programs at risk? If you answer "yes" to any of the following questions, you have a potential security risk.

Have you acquired any new programs within the last year?

Do you use your computer to communicate electronically with other computers?

Do you ever receive programs or data from other people?

Is there any significant program or data item of which you do not have a second copy?

Relax; you are not alone. Most computer users have a security risk. Being at risk does not mean you should stop using computers. It does mean you should learn more about the risk you face, and how to control that risk. 

Users and managers of large mainframe computing systems of the 1960s and l970s developed computer security techniques that were reasonably effective against thethreatsof that era. However, two factors have made those security procedures outdated: 

Personal computer use. Vast numbers of people have become dedicated users of personal computing systems, both for business and pleasure. We try to make applications "user friendly" so that computers can be used by people who know nothing of hardware or programming, just as people who can drive a car do not need to know how to design an engine. Users may not be especially conscious of the security threats involved in computer use; even users who are aware may not know what to do to reduce their risk. 

Networked remote-access systems. Machines are being linked in large numbers. The Internet and its cousin, the World-Wide Web, seem to double every year in number of users. A user of a mainframe computer may not realize that access to the same machine is allowed to people throughout the world from an almost uncountable number of computing systems. 

Every computing professional must understand the threats and the countermeasures currently available in computing. This book addresses that need. 

This book is designed for the student or professional in computing. Beginning at a level appropriate for an experienced computer user, this book describes the security pitfalls inherent in many important computing tasks today. Then, the book explores the controls that can check these weaknesses. The book also points out where existing controls are inadequate and serious consideration must be given to the risk present in the computing situation. 

Uses of This Book

The chapters of this book progress in an orderly manner. After an introduction, the topic of encryption, the process of disguising something written to conceal its meaning, is presented as the first tool in computer security. The book continues through the different kinds of computing applications, their weaknesses, and their controls. 
The applications areas include:
general programs 
operating systems 
data base management systems 
remote access computing 
multicomputer networks 

These sections begin with a definition of the topic, continue with a description of the relationship of security to the topic, and conclude with a statement of the current state of the art of computer security research related to the topic. The book concludes with an examination of risk analysis and planning for computer security, and a study of the relationship of law and ethics to computer security. 

Background required to appreciate the book is an understanding of programming and computer systems. Someone who is a senior or graduate student in computer science or a professional who has been in the field for a few years would have the appropriate level of understanding. Although some facility with mathematics is useful, all necessary mathematical background is developed in the book. Similarly, the necessary material on design of software systems, operating systems, data bases, or networks is given in the relevant chapters. One need not have a detailed knowledge of these areas before reading this book. 

The book is designed to be a textbook for a one- or two-semester course in computer security. The book functions equally well as a reference for a computer professional. The introduction and the chapters on encryption are fundamental to the understanding of the rest of the book. After studying those pieces, however, the reader can study any of the later chapters in any order. Furthermore, many chapters follow the format of introduction, then security aspects of the topic, then current work in the area. Someone who is interested more in background than in current work can stop in the middle of one chapter and go on to the next. 

This book has been used in classes throughout the world. Roughly half of the book can be covered in a semester. Therefore, an instructor can design a one-semester course that considers some of the topics of greater interest. 

What Does This Book Contain?

This is the revised edition of Security in Computing. It is based largely on the previous version, with many updates to cover newer topics in computer security. Among the salient additions to the new edition are these items: 

Viruses, worms, Trojan horses, and other malicious code. Complete new section (first half of Chapter 5) including sources of these kinds of code, how they are written, how they can be detected and/or prevented, and several actual examples. 

Firewalls. Complete new section (end of Chapter 9) describing what they do, how they work, how they are constructed, and what degree of protection they provide. 

Private e-mail. Complete new section (middle of Chapter 9) explaining exposures in e-mail, kind of protection available, PEM and PGP, key management, and certificates. 

Clipper, Capstone, Tessera, Mosaic, and key escrow. Several sections, in Chapter 3 as an encryption technology, and Chapter 4 as a key management protocol, and in Chapter 11 as a privacy and ethics issue. 

Trusted system evaluation. Extensive addition (in Chapter 7) including criteria from the United States, Europe, Canada, and the soon-to-be-released Common Criteria. 

Program development processes, including ISO 9000 and the SEI CMM. A major section in Chapter 5 gives comparisons between these methodologies. 

Guidance for administering PC, Unix, and networked environments. In addition to these major changes, there are numerous small changes, ranging from wording changes to subtle notational changes for pedagogic reasons, to replacement, deletion, rearrangement, and expansion of sections. 

The focus of the book remains the same, however. This is still a book covering the complete subject of computer security. The target audience is college students (advanced undergraduates or graduate students) and professionals. A reader is expected to bring a background in general computing technology; some knowledge of programming, operating systems, and networking is expected, although advanced knowledge in those areas is not necessary. Mathematics is used as appropriate, although a student can ignore most of the mathematical foundation if he or she chooses. 

Acknowledgments

Many people have contributed to the content and structure of this book. The following friends and colleagues have supplied thoughts, advice, challenges, criticism, and suggestions that have influenced my writing of this book: Lance Hoffman, Marv Schaefer, Dave Balenson, Terry Benzel, Curt Barker, Debbie Cooper, and Staffan Persson. Two people from outside the computer security community were very encouraging: Gene Davenport and Bruce Barnes. I apologize if I have forgotten to mention someone else; the oversight is accidental. 

Lance Hoffman deserves special mention. He used a preliminary copy of the book in a course at George Washington University. Not only did he provide me with suggestions of his own, but his students also supplied invaluable comments from the student perspective on sections that did and did not communicate effectively. I want to thank them for their constructive criticisms. 

Finally, if someone alleges to have written a book alone, distrust the person immediately. While an author is working 16-hour days on the writing of the book, someone else needs to see to all the other aspects of life, from simple things like food, clothing, and shelter, to complex things like social and family responsibilities. My wife, Shari Lawrence Pfleeger, took the time from her professional schedule so that I could devote my full energies to writing. Furthermore, she soothed me when the schedule inexplicably slipped, when the computer went down, when I had writerOs block, or when some other crisis beset this project. On top of that, she reviewed the entire manuscript, giving the most thorough and constructive review this book has had. Her suggestions have improved the content, organization, readability, and overall quality of this book immeasurably. Therefore, it is with great pleasure that I dedicate this book to Shari, the other half of the team that caused this book to be written. 

Charles P. Pfleeger Washington DC

Security in Computing

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.

Small Ramsey Numbers

Let denote the class of all graphsG which satisfyG→(G
1,G
2). As a way of measuring minimality for members of
 , we define thesize Ramsey number ř(G
1,G
2) by
 . We then investigate various questions concerned with the asymptotic behaviour ofř.

The size ramsey number

Claw-free graphs—a survey

All Ramsey numbers for cycles in graphs

Given a family of (hyper)graphs $\mathcal{F}$ a (hyper)graph $G$ is said to be $\mathcal{F}$-saturated if $G$ is $F$-free for any $F \in\mathcal{F}$ but for any edge e in the complement of $G$ the (hyper)graph $G + e$ contains some $F\in\mathcal{F}$. We survey the problem of determining the minimum size of an $\mathcal{F}$-saturated (hyper)graph and collect many open problems and conjectures.

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Ralph J. Faudree

Papers

The size ramsey number

Claw-free graphs—a survey

All Ramsey numbers for cycles in graphs

A Survey of Minimum Saturated Graphs

Path Ramsey numbers in multicolorings