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 anAssociate Professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. His research interests are graph theory, combinatorics, and discrete mathematics.

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

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).