RobertsonSeymour

RobertsonSeymour refers to the collaboration between mathematicians Neil Robertson and Paul Seymour, renowned for their work on graph minors and the resulting body of the Graph Minors Project. The most famous outcome of this collaboration is the Robertson–Seymour Graph Minors Theorem, a cornerstone of structural graph theory that has influenced both theory and algorithms.

The Graph Minor Theorem states that finite graphs are well-quasi-ordered under the minor relation: in any infinite sequence of finite graphs, there exist indices i < j such that G_i is a minor of G_j. This result implies that for any fixed graph H, the class of graphs not containing H as a minor can be characterized by a finite set of forbidden minors. More broadly, many minor-closed properties have finite obstruction sets, and the project offered a deep structural understanding of how graphs excluding a fixed minor can be decomposed into pieces with controllable complexity.

The Robertson–Seymour project, pursued over several decades beginning in the 1980s, produced a comprehensive framework for minor theory, including a detailed structure theorem describing how graphs excluding a fixed minor can be assembled from nearly embeddable components. The work has had a lasting impact on graph theory, informing advances in algorithm design, graph coloring, planarity, and topological graph theory, and it remains one of the most influential achievements in combinatorics.