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.