# The Strong Perfect Graph Theorem

@article{Chudnovsky2002TheSP, title={The Strong Perfect Graph Theorem}, author={M. Chudnovsky and Neil Robertson and Paul D. Seymour and Robin Thomas}, journal={Annals of Mathematics}, year={2002}, volume={164}, pages={51-229} }

A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. The ?strong perfect graph conjecture? (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by Conforti, Cornu?ejols and Vuiskovi?c ? that every Berge graph either falls into one of a few basic…

## 737 Citations

Progress on perfect graphs

- MathematicsMath. Program.
- 2003

The main aspects of perfect graphs and their relevance are surveyed and the recent proof of the Strong Perfect Graph Conjecture of Berge from 1961 is outlined.

Odd Pairs of Cliques

- Mathematics
- 2006

A graph is Berge if it has no induced odd cycle on at least 5 vertices and no complement of induced odd cycle on at least 5 vertices. A graph is perfect if the chromatic number equals the maximum…

The perfection and recognition of bull-reducible Berge graphs

- MathematicsRAIRO Theor. Informatics Appl.
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This paper gives a simple proof that every bull-reducible Berge graph is perfect and leads to a recognition algorithm for this new class of perfect graphs whose complexity, O(n 6 ) , is much lower than that announced for perfect graphs.

Forbidden Induced Subgraphs of Double-split Graphs

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This work finds the forbidden induced subgraph characterization of doubled graphs; it contains 44 graphs and is the first of its kind.

Towards a constructive formalization of Perfect Graph Theorems

- MathematicsICLA
- 2019

This paper model finite simple graphs in the constructive type theory of Coq Proof Assistant without adding any axiom to it and uses this framework to present a constructive proof of the Lovasz Replication Lemma, which is the central idea in the proof of Weak Perfect Graph Theorem.

Chromatic number and subtrees of graphs

- Mathematics
- 2017

Let G and H be two graphs. We say that G induces H if G has an induced subgraph isomorphic to H: A. Gyárfás and D. Sumner, independently, conjectured that, for every tree T. there exists a function…

A new decomposition theorem for Berge graphs

- Mathematics
- 2005

A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas…

Partial characterizations of clique-perfect and coordinated graphs: superclasses of triangle-free graphs

- MathematicsElectron. Notes Discret. Math.
- 2008

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