Favorite conjectures and open problems
著者
書誌事項
Favorite conjectures and open problems
(Problem books in mathematics / edited by K. Bencsáth and P.R. Halmos, . Graph theory)
Springer, c2016-
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- 2
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注記
Series editor: Peter Winkler
Editors of 2: Ralucca Gera, Teresa W. Haynes, Stephen T. Hedetniemi
LCCN of 2: 2018959757
Includes bibliographical references
内容説明・目次
- 巻冊次
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1 ISBN 9783319319384
内容説明
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.
目次
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).- Chvatal'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).
- 巻冊次
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2 ISBN 9783319976846
内容説明
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.
目次
1. Desert Island Conjectures (L.W. Beineke).- 2. Binding Number, Cycles and Cliques ( W. Goddard).- 3. On a Conjecture Involving Laplacian Eigenvalues of Trees (D. P. Jacobs and V. Trevison).- 4. Queens Around the World in Twenty-five Years ( D. Weakley).- 5. Reflections on a Theme of Ulam (R.Graham).- 6. Ulam Numbers of Graphs (S.T. Hedetniemi).- 7. Forbidden Trees (D. Sumner).- 8. Some of My Favorite Conjectures: Local Conditions Implying Global Cycle Properties (O. Oellermann).- 9. The Path Partition Conjecture (M. Frick and J. E. Dunbar).- 10. To the Moon and Beyond (E. Gethner).- 11. My Favorite Domination Game Conjectures (M. A. Henning).- 12. A De Bruijn-Erdos theorem in graphs? (V. Chvatal).- 13. An Annotated Glossary of Graph Theory Parameters, with Conjectures (R. Gera, T. W. Haynes, S. T. Hedetniemi, and M. A. Henning).
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