Graph minor theory. The first success of this theory was the proof of Wagner's conjecture that in every infinite set of finite graphs, one is a minor of the other. However, the theory developed over the course of twenty-odd papers by Robertson and Seymour has been enormously fruitful and its consequences are still being actively explored, with no end in sight. The proof of the strong perfect graph conjecture was the next spectacular success, and then came applications to the structure of clawfree graphs. Graph minor theory almost singlehandedly transformed people's perception of graphs as structureless combinatorial gadgets about which only countless ad hoc theorems could be proved, into a realization that graphs are highly structured objects about which general theories can be developed.
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