© 2018

Graph Theory

Favorite Conjectures and Open Problems - 2

  • Ralucca Gera
  • Teresa W. Haynes
  • Stephen T. Hedetniemi
  • Describes the origin and history behind conjectures and problems in graph theory

  • Provides various methods to solving research problems in the field

  • Provides strong pedagogical content for graduate students and a reference to researchers in the field

  • Includes an annotated glossary of nearly 300 parameters and 600 references


Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Ralucca Gera, Stephen T. Hedetniemi, Teresa W. Haynes
    Pages 1-5
  3. Lowell W. Beineke
    Pages 7-18
  4. Wayne Goddard
    Pages 19-25
  5. David P. Jacobs, Vilmar Trevisan
    Pages 27-42
  6. William D. Weakley
    Pages 43-54
  7. Ron Graham
    Pages 55-61
  8. Stephen T. Hedetniemi
    Pages 63-68
  9. David Sumner
    Pages 69-89
  10. Marietjie Frick, Jean E. Dunbar
    Pages 101-113
  11. Ellen Gethner
    Pages 115-133
  12. Michael A. Henning
    Pages 135-148
  13. Vašek Chvátal
    Pages 149-176
  14. Ralucca Gera, Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning
    Pages 177-281

About this book


This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate students and established researchers in discrete mathematics who are searching for research ideas and references. Each chapter provides more than a simple collection of results on a particular topic; it captures the reader’s interest with techniques that worked and failed in attempting to solve particular conjectures. The history and origins of specific conjectures and the methods of researching them are also included throughout this volume. Students and researchers can discover how the conjectures have evolved and the various approaches that have been used in an attempt to solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and over 600 references is also included in this volume. This glossary provides an understanding of parameters beyond their definitions and enables readers to discover new ideas and new definitions in graph theory.

The editors were inspired to create this series of volumes by the popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,” which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January 2014, at which many of the best-known graph theorists spoke. In an effort to aid in the creation and dissemination of conjectures and open problems, which is crucial to the growth and development of this field, the editors invited these speakers, as well as other experts in graph theory, to contribute to this series.


Coloring and Domination Digraphs Erdos Graph Eigenvalues Graph Theory conjectures open problems Desert Island Conjectures Binding Number Cliques Laplacian Eigenvalues of Trees Ulam Numbers Global Cycle Properties Path Partition Conjecture Domination Game Conjectures

Editors and affiliations

  • Ralucca Gera
    • 1
  • Teresa W. Haynes
    • 2
  • Stephen T. Hedetniemi
    • 3
  1. 1.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA
  2. 2.Department of MathematicsEast Tennessee State UniversityJohnson CityUSA
  3. 3.School of ComputingClemson UniversityClemsonUSA

About the editors

Ralucca Gera is the Associate Provost for Graduate Education and Professor of Mathematics in the Applied Math Department at the Naval Postgraduate School.  She is also a researcher in the Center for Cyber Warfare at the Naval Postgraduate School and the Network Science Center at United States Military Academy.  Her research interests include graph theory, network science, machine learning and artificial intelligence.

Stephen T. Hedetniemi is a Professor Emeritus in the School of Computing at Clemson University. His research interests include graph theory, graph algorithms, and computational complexity.

Teresa W. Haynes is a Professor of Mathematics at East Tennessee State University and a Visiting Professor at the University of Johannesburg, South Africa. Her research interest is graph theory.

Bibliographic information