Graph Theory

Favorite Conjectures and Open Problems - 1

Ralucca Gera, Stephen Hedetniemi, Craig Larson

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English

Springer International Publishing AG
23 June 2018

Discrete mathematics; Algebra; Combinatorics & graph theory; History of mathematics

Series: Problem Books in Mathematics

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.

Edited by: Ralucca Gera, Stephen Hedetniemi, Craig Larson
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2016
Dimensions: Height: 235mm, Width: 155mm, Spine: 16mm
Weight: 4.628kg
ISBN: 9783319811598
ISBN 10: 3319811592
Series: Problem Books in Mathematics
Pages: 291
Publication Date: 23 June 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Highly Irregular (G. Chartrand).- Hamiltonian Extension (P. Zhang).- On Some Open Questions for Ramsey and Folkman Numbers (S. Radziszowski and X. Xu).- All my favorite conjectures are critical(T. Haynes).- The local representation of graph conjecture(E. Scheinerman).- Some of My Favorite Coloring Problems for Graphs and Digraphs (J. Gimble).- My Top 10 Favorite Conjectures and Open Problems(S. Hedetniemi).- Chvátal's t0-tough conjecture (L. Lesniak).- What do Trees and Hypercubes have in Common (H. Mulder).- Two chromatic conjectures: one for vertices, one for edges (M. Kayll).- Some Conjectures and Questions in Chromatic Topological Graph Theory (J. Hutchinson).- Turan's Brick factory problem (L. Szekely). -It is all labeling (P. Slater).- My Favorite Domination Conjectures (M. Henning).- Circuit Double Covers of Graphs (C. Zhang).

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.

Reviews for Graph Theory: Favorite Conjectures and Open Problems - 1

The title is accurate. This is a collection of 16 independent papers by 17 authors. Each of these chapters is self-contained and can be understood by readers with no more than an undergraduate class in graph theory. ... The format and accessibility of the book make it a good choice for a course or seminar in which each student can present a chapter. (Miklos Bona, MAA Reviews, maa.org, February, 2017)