Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of 'computerised' society for which traditional areas of mathematics such as algebra or calculus are powerless.

This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking the courses in graph theory, discrete mathematics, data structures, algorithms.It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text.

The book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring.The reader is conducted from the simplest examples, definitions and concepts, step by step, towards an understanding of a few most fundamental facts in the field.

About the author

Vitaly I. Voloshin is a professor at the Department of Mathematics and Statistics, Troy University. He worked at Moldova State University and at the Institute of Mathematics and Informatics of the Moldovan Academy of Sciences (Republic of Moldova, former Soviet Union) for many years, and moved to the United States in 2002. His research areas include graph and hypergraph coloring, theory, algorithms and applications.

In 1993, he originated the direction of mixed hypergraph coloring, and there are now more than 200 scientific publications on the subject, including the author's Fields Institute Monograph. His research has been repeatedly supported by many scientific foundations of Italy, Germany, Canada, China, the United States, and other countries. He was the invited speaker of many major international conferences, held visiting positions at many universities throughout the world, and supervised and was consulted on many MS and PhD theses.

http://spectrum.troy.edu/voloshin/