Strong Perfect Graph Theorem
The Strong Perfect Graph Theorem states that a graph is perfect if and only if it does not contain any induced subgraphs that are either an odd cycle of length five or more, or the complement of such a cycle. A graph is considered perfect if, for every induced subgraph, the size of the largest clique equals the size of the smallest coloring.
This theorem was proven by Maria Chudnovsky, Nina Robertson, Paul Seymour, and Robin Thomas in 2006. It has significant implications in graph theory, particularly in understanding the structure of perfect graphs and their applications in optimization problems.