perfect graph

It is also a 4-vertex-connected and 4-edge-connected perfect graph.

Skew partitions play an important role in the theory of perfect graphs.

The full conjecture is a corollary of the strong perfect graph theorem.

This was one of the results that motivated the initial definition of perfect graphs.

Some of the more well-known perfect graphs are:

Open problems on perfect graphs, maintained by the American Institute of Mathematics.

Skew partitions were introduced by , in connection with perfect graphs.

Alfred Lehman for 0,1-matrix analogues of the theory of perfect graphs.

Chordal graphs are a subclass of the well known perfect graphs.

The 1972 paper by László Lovász made a breakthrough in the study of perfect graphs.

The trivially perfect graphs are the comparability graphs of rooted trees.

For many years the complexity of recognizing Berge graphs and perfect graphs remained open.

Every perfectly orderable graph is a perfect graph.

The perfect graphs are those for which this lower bound is tight, not just in the graph itself but in all of its induced subgraphs.

In his initial work on perfect graphs, Berge made two important conjectures on their structure that were only proved later.

Reed's thesis research concerned perfect graphs.

The second theorem, conjectured by Berge, provided a forbidden graph characterization of the perfect graphs.

He is particularly remembered for two conjectures on perfect graphs that he made in the early 1960s but were not proved until significantly later:

Thus, the complementation property of perfect graphs can provide an alternative proof of Dilworth's theorem.

By the perfect graph theorem, the complement of G (an "odd antihole") must therefore also not be perfect.

Chromatic number, cliques, and perfect graphs, pp.

They play an important role in Lovász's celebrated proof of the perfect graph theorem (Golumbic, 1980).

For perfect graphs, it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming.

Mirsky's theorem and Dilworth's theorem are also related to each other through the theory of perfect graphs.

Parthasarathy is known for his work (with his student G. Ravindra) on strong perfect graph conjecture.