Neil Robertson completed his PhD in 1969 under the supervision of Bill Tutte. The title of his thesis is "Graphs Minimal under Girth, Valency and Connectivity Constraints". He then joined the faculty at Ohio State University, where he was awarded the title of Distinguished Professor in 2006. At Ohio State, he supervised the research of 19 PhD students.
Neil is renowned for his work in graph theory. Best known is his series of remarkable research papers with Paul Seymour that proved the Graph Minors Theorem, which states that the set of undirected graphs, partially ordered by the graph minor relationship, form a well-quasi-ordering. This result is now known as the Robertson-Seymour Theorem. In 1996, Neil together with Daniel Sanders, Paul Seymour, and Robin Thomas, published a simpler proof of the four colour theorem. In 2006, Neil together with Maria Chudnovsky, Paul Seymour, and Robin Thomas, published a proof of the strong perfect graph conjecture, thereby resolving one of the famous open problems in graph theory that had been proposed by Claude Berge in 1961.
Neil is a three-time winner of the Fulkerson Prize. He received the prize in 1994 for his work (with Paul Seymour and Robin Thomas) on the Hadwiger conjecture, in 2006 for the Robertson-Seymour theorem, and in 2009 for the proof of the strong perfect graph conjecture. He also received the Polya Prize in 2004 for the Robertson-Seymour theorem. In 2002, Neil received the Faculty of Mathematics Alumni Achievement Award in recognition of his outstanding contributions to graph theory.