A Tour Through Graph Theory

Graph theory is an area of mathematics that can challenge one's notions of what mathematics is and can be. The author discovered this as a student, as her discovery led her to pursue an advanced degree in mathematics. In A Tour through Graph Theory, Second Edition, the author shares her enthusiasm for the topic with students assuming only high school mathematics experience.

The book introduces graph theory to students who are not mathematics majors. To distinguish itself from others covering the same topic, the book:

• Employs graph theory to teach mathematical reasoning
• Promotes critical thinking and problem solving
• Provides rich examples and clear explanations without using proofs
• Includes thoughtful discussions of historical problems and modern questions

New to this edition, the author offers more explanation for concepts or adds more context for the topics. Significant care was taken in modifying the description and examples for the more complex algorithms and theoretical discussions. More than 40 new exercises have been added, and 50 additional graphs have been added to existing exercises to provide more options for homework or quiz problems.

This book is intended to strike a balance between focusing on the theory and exploration of proof techniques and the algorithmic aspect of graph theory. Explanations and logical reasoning for solutions, but no formal mathematical proofs, are provided. Each chapter includes problems to test understanding of the material and can be used for homework, quiz problems, or self-study.

Karin R. Saoub is the M. Paul Capp and Constance Whitehead Professor of Mathematics and Dean of the School of Health, Science, and Sustainability at Roanoke College, Salem, VA. She earned her PhD in mathematics from Arizona State University and a BA from Wellesley College. Her research focuses on graph coloring and online algorithms applied to tolerance graphs. She is also the author of Graph Theory: An Introduction to Proofs, Algorithms, and Applications, published by CRC Press.