Overview
- 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
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (16 chapters)
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Front Matter
Keywords
- Erdos
- coloring and domination
- digraphs
- graph eigenvalues
- graph theory conjectures
- open problems
- Ramsey and Folkman Numbers
- Hamiltonian Extension
- Trees and Hypercubes
- chromatic conjectures
- Chromatic Topological Graph Theory
- Domination Conjectures
- Circuit Double Covers of Graphs
- combinatorics
- matrix theory
About this book
This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm.
The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.
Reviews
Editors and Affiliations
About the editors
Ralucca Gera is an Associate Professor of Mathematics and a researcher in the Center for Cyber Warfare at the Naval Postgraduate School, as well as the Network Science Center at United States Military Academy. Her research interests are in graph theory and network science.
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.
Craig Larson is an Associate Professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. His research interests are graph theory, combinatorics, and discrete mathematics.
Bibliographic Information
Book Title: Graph Theory
Book Subtitle: Favorite Conjectures and Open Problems - 1
Editors: Ralucca Gera, Stephen Hedetniemi, Craig Larson
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-319-31940-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-31938-4Published: 28 October 2016
Softcover ISBN: 978-3-319-81159-8Published: 23 June 2018
eBook ISBN: 978-3-319-31940-7Published: 19 October 2016
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XII, 291
Number of Illustrations: 90 b/w illustrations, 24 illustrations in colour
Topics: Graph Theory, Combinatorics, Linear and Multilinear Algebras, Matrix Theory, History of Mathematical Sciences