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Harary Memorial Lecture Saturday 11:20–12:20 109 Oelman Hall Recent results on graph searching Derek Corneil University of Toronto Abstract Searching a graph is a fundamental operation that is the cornerstone of many graph algorithms. In the early 1970s most graph searching was either Breadth First Search (BFS) or Depth First Search (DFS). Later, Lexicographic BFS (LBFS) was introduced as a simple linear time algorithm to recognize chordal graphs. Somewhat surprisingly, LBFS was largely ignored until the 1990s, when it was shown to be useful for various problems on restricted families of graphs. In particular, LBFS was applied in a multi-sweep fashion where ties of which vertex to choose next were broken by appealing to a previous sweep. Correctness proofs of many of these algorithms used an elegant 4-vertex condition that characterizes vertex orderings that are LBFS orderings. Since the late 1990s, many new applications of LBFS have appeared. Furthermore, similar 4-vertex characterizations have been discovered for other graph searches such as BFS, DFS and Lexicographic DFS. In this talk, we will give an overview of this work, as well as a summary of open problems. 10
Conference Honorees Terry McKee Following his mathematics Ph.D. in 1974 at Wisconsin, Dr. Terry A. McKee was at Western Illinois University for two years. The rest of his career has been right here at Wright State, including milestones in 1979 (promotion to Associate Professor), 1981 (tenure), and 1985 (promotion to Professor). Over the years, Terry’s path of scholarship has taken him from model theory in mathematical logic, the field of his doctoral studies and one of the most abstract in all of mathematics, to graph theory in discrete mathematics, one of the most readily applicable and accessible branches of our subject. His prolific record of research has produced (so far) over 100 published articles and garnered nearly a decade of funding from the Office of Naval Research. Terry is likewise a smashing success in the classroom. In fact, his outstanding teaching was recognized in awards from the College of Science and Mathematics, the President of Wright State University, the WSU Alumni Association, and SOCHE - the Southwestern Ohio Council for Higher Education. In 1991, Terry garnered the Presidential Award for Outstanding Faculty Member university-wide. Ten years later, he was tapped to become Associate Dean, a position Terry held until his midsummer retirement. Thus, Terry’s career at Wright State has spanned thirty years, throughout which he has been active and productive in research. Happily for the department that productivity will continue, and will continue here, as Terry has moved back to the department from the CoSM offices and is banging away today on his graph theory. A telling note about the man appears on the wall of his small, windowless office - not the teaching awards, not the certificates recognizing his decades on the faculty, not even his Presidential Award. Instead, we see a plaque bearing his name from Dayton’s Community Blood Center, thanking him for being a ten-gallon blood donor. Manley Perkel Dr. Manley Perkel, a native of South Africa, completed his mathematics Ph.D. at Michigan in 1977. In a manner of speaking, he then followed in Terry’s footsteps, taking a faculty position at Western Illinois and thence coming to Wright State. Following his initial appointment in 1978, Manley earned promotion to Associate Professor with tenure in 1985 and promotion to Professor in 1995. Exemplary teaching has been a hallmark of Manley’s career from start to finish. Indeed, while he was still an Assistant Professor, he won an award for outstanding teaching from what was then WSU’s College of Science and Engineering; and also in his very last years he won one of the 2005-2006 College of Science and Mathematics Outstanding Teaching Awards. A student in his Spring 2006 Modern Algebra class who heard of his forthcoming retirement wrote on an evaluation form, ”Don’t let him retire! Give him all the money he wants. Throw in a bigger office and a car, too.” Manley’s scholarship, focused on algebra, combinatorics, and graph theory, has taken him far and wide over the years. For example, on a six-week visit to Australia and New Zealand, he lectured at universities in Perth, Adelaide, Melbourne, Canberra, Sydney, and Auckland - and took a gigantic bungee jump along the way, the photographic proof of which resides on his office wall. Moreover, 11
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