In 1969, Robertson joined the faculty of the Ohio State University, where he was promoted to Associate Professor in 1972 and Professor in 1984. He was a consultant with Bell Communications Research from 1984 to 1996. He has held visiting faculty positions in many institutions, most extensively at Princeton University from 1996 to 2001, and at Victoria University of Wellington, New Zealand, in 2002. He also holds an adjunct position at
King Abdulaziz University in
Saudi Arabia.[2]
Research
Robertson is known for his work in
graph theory, and particularly for a long series of papers co-authored with
Paul Seymour and published over a span of many years, in which they proved the
Robertson–Seymour theorem (formerly Wagner's Conjecture).[5] This states that families of graphs closed under the
graph minor operation may be characterized by a
finite set of
forbidden minors. As part of this work, Robertson and Seymour also proved the
graph structure theorem describing the graphs in these families. [6]
Additional major results in Robertson's research include the following:
In 1996, Robertson, Seymour, Thomas, and
Daniel P. Sanders published a new proof of the
four color theorem,[9] confirming the Appel–Haken proof which until then had been disputed. Their proof also leads to an efficient
algorithm for finding 4-colorings of planar graphs.
Robertson has won the
Fulkerson Prize three times, in 1994 for his work on the Hadwiger conjecture, in 2006 for the Robertson–Seymour theorem, and in 2009 for his proof of the strong perfect graph theorem.[11]
He also won the
Pólya Prize (SIAM) in 2004, the OSU Distinguished Scholar Award in 1997, and the Waterloo Alumni Achievement Medal in 2002. In 2012 he became a fellow of the
American Mathematical Society.[12]