Bulletin of the American Mathematical Society

Author(s): László Lovász
Journal: Bull. Amer. Math. Soc. 43 (2006), 75-86.
MSC (2000): Primary 05C83
Posted: October 24, 2005
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Abstract: A monumental project in graph theory was recently completed. The project, started by Robertson and Seymour, and later joined by Thomas, led to entirely new concepts and a new way of looking at graph theory.

The motivating problem was Kuratowski's characterization of planar graphs, and a far-reaching generalization of this, conjectured by Wagner: If a class of graphs is minor-closed (i.e., it is closed under deleting and contracting edges), then it can be characterized by a finite number of excluded minors. The proof of this conjecture is based on a very general theorem about the structure of large graphs: If a minor-closed class of graphs does not contain all graphs, then every graph in it is glued together in a tree-like fashion from graphs that can almost be embedded in a fixed surface.

We describe the precise formulation of the main results and survey some of its applications to algorithmic and structural problems in graph theory.

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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 05C83

László Lovász
Affiliation: Microsoft Research, Redmond, Washington 98052

DOI: 10.1090/S0273-0979-05-01088-8
PII: S 0273-0979(05)01088-8
Received by editor(s): June 6, 2005,
Received by editor(s) in revised form: August 9, 2005
Posted: October 24, 2005
Additional Notes: This article is based on a lecture presented January 7, 2005, at the AMS Special Session on Current Events, Joint Mathematics Meetings, Atlanta, GA.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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