Graph Theory: Favorite Conjectures and Open Problems - 1

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 the Associate Provost for Graduate Education and Professor of Mathematics in the Applied Math Department at the Naval Postgraduate School. She is also a researcher in the Center for Cyber Warfare at the Naval Postgraduate School and the Network Science Center at United States Military Academy. Her research interests include graph theory, network science, machine learning and artificial intelligence.

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.

Teresa W. Haynes is a Professor of Mathematics at East Tennessee State University and a Visiting Professor at the University of Johannesburg, South Africa. Her research interest is graph theory.

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.

Stephen T. Hedetniemi is one of the earliest pioneers of domination in graphs along with E. J. Cockayne, who together proposed the theory of domination in graphs, in one of the most cited papers in the field in 1977.  He received his PhD from the University of Michigan in 1966, with two world-class advisors, graph theorist Frank Harary, and the pioneer of genetic algorithms and MacArthur Fellowship winner, John Holland.  He coauthored, the first book on domination in 1988 Fundamentals of Domination in Graphs, and co-edited a second book, Domination in Graphs: Advanced Topics. He also co-edited  2 volumes in Springer’s Problem Books in Mathematics  Graph Theory: Favorite Conjectures and Open Problems. Since 1974 he has coauthored more than 300 papers, 180 of which are on domination and domination-related concepts.  Hedetniemi has introduced some of the most-studied concepts in domination theory, including total domination, independent domination, irredundance, Roman domination, power domination, alliances in graphs, signed and minus domination, fractional domination, domatic numbers, domination in grid graphs and chessboards, the first domination algorithms, the first domination NP-completeness results, and the first self-stabilizing domination algorithms.  After leaving the University of Michigan, he taught computer science at the University of Iowa, and the University of Virginia, spent a visiting year at the University of Victoria with E. J. Cockayne, and then became department head of Computer and information Science at the University of Oregon.  Since 1982 has been at Clemson University, where he served a five-year term as department head, and served on the Executive Committee of the Computing Accreditation Commission of ABET, Inc. He is currently Emeritus Professor of Computer Science in the School of Computing at Clemson University.