For every graph $ G $ with chromatic number $ \\chi(G) $ and clique number $ \\ omega(G) $ , it is folklore that $ \\chi(G) \\geq \\omega (G) $ . The latter inequality naturally gives rise to two questions. First, for which graphs the chromatic number matches the clique number? Since the disjoint union of every graph $ G $ and a complete graph on $ \\chi (G) $ vertices results in a graph whose chromatic number equals its clique number , it would be sensible (and also promising) to ask for graphs whose all induced subgraphs possess chromatic number and clique number equal. Such graphs are called `` perfect quot;, firstly introduced by the French mathematician Claude Berge, and play an immensely important role in combinatorial optimization and theoretical computer science. One neater way to put the notion of perfection is utilizing the concept of an ``ideal quot; , i.e. a family of graphs closed under taking induced subgraphs. Therefore indeed the first question (in its more reasonable form) asks for a characterization of the ideal of perfect graphs, which is precisely done by the celebrated ``strong perfect graph theorem quot;. This theorem describes all minimally imperfect graphs (i.e. graphs which do not belong to the ideal of perfect graphs where all their induced subgraphs do so), asserting that odd cycles of length at least five and their complements are actually the only ones.