BOOKS

(with W.J. Adams and A. Gewirtz) Elements of Linear Programming. Van Nostrand Reinhold, New York (1969).

(with L. Auslander, F.J. Avenoso, P.M. Cheifetz, E. Dyer, A. Gewirtz, B.E. Hunte, and H.E. Rauch) Mathematics Through Statistics. Mathematical Dimensions, Inc., Chicago (1971).

(with J. Blamire, R.A. Eckhardt, and A. Gewirtz) Wordprocessing for the TRS 80 and SuperScipsit. Thorin Partners, New York (1983).

(with K.T. Balińska) Random Graphs with Bounded Degree. Publishing House of the Poznań University of Technology, Poznań (2006).

  • Pre-publication Editions as Models for random graphs with bounded degree, August 2003, 2004.
  • Description: K.T. Balińska and L.V. Quintas, Random Graphs with Bounded Degree

Initiated in the 1980s, the study of random graphs with bounded degree has developed into an important branch of discrete mathematics as an intersection of graphs theory, combinatorics, and probability and has applications to chemistry, physics, biology, and computer science.

This is the first book that provides a comprehensive overview of this field. Based on the investigations carried out by the authors over a number of years, it contains a detailed description of probability models, the known results, and techniques used.

The fundamental model studied in this book is a random process for graphs with  bounded degree. Graph-theoretical and probabilistic properties of its transition digraph with nodes corresponding to graphs with bounded degree are presented.

Among techniques used there are the classical tools of graph theory, a new method of solving asymptotic graph problems, and several exact and randomized combinatorial algorithms.

The unique strength of this book is how it can be used in a variety of ways so that it should be of interest to undergraduates, graduate students, and researchers. Specifically the book can be used as an introduction to graph theory smoothly leading into topics involving algorithmic computer science and random graph processes. These topics are then investigated at the intermediate level with many illustrative exercises and figures culminating with open problems at both the doctoral studies level and some suitable for advanced researchers.

Contents:

1. Introduction

2. Graphs and random graphs

3. Edge maximal f-graphs

4. The random f-graph process with f = 2

5. The random f-graph process with f ≥ 3

6. The order and size of D(n, f)

7. Maximum degrees in D(n, f)

8. Distance properties of U(n, f)

9. Hamilton paths in U(n, f)

10 Graph processes as Markov chains

11. The kinetic approach

12. The uniform model for edge maximal f-graphs

13. Applications

14. Solutions

Appendix: Tables and Figures. References. Index of definitions. Index of symbols.

Authors: Krystyna T. Balińska is a Professor of Computer Science at the Technical University of Poznań, Poland. Louis V. Quintas studied at Columbia University and then specializing in graph theory earned a Ph.D. in mathematics at the City University of New York. He is a Professor of Mathematics at Pace University, New York, U.S.A.