In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither...

perfect graph theorem states that the complement graph of a perfect graph is also perfect. The strong perfect graph theorem characterizes the perfect...

In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph...

see orientation. 2.  For the strong perfect graph theorem, see perfect. 3.  A strongly regular graph is a regular graph in which every two adjacent vertices...

in 1976, long before the proof of the strong perfect graph theorem completely characterized the perfect graphs. The same result was independently discovered...

to the strong perfect graph theorem, the perfect graphs have a forbidden graph characterization resembling that of bipartite graphs: a graph is bipartite...

Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006), "The strong perfect graph theorem" (PDF), Annals of Mathematics, 164 (1): 51–229, arXiv:math/0212070v1...

Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006), "The strong perfect graph theorem", Annals of Mathematics, 164 (1): 51–229, arXiv:math/0212070...

graph introduced by Shannon. The conjecture remained unresolved for 40 years, until it was established as the celebrated strong perfect graph theorem...

complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only...

stated as follows: Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each...

induced subgraph. It is now known (the strong perfect graph theorem) that perfect graphs may be characterized as the graphs that do not have as induced subgraphs...

2006 for the Robertson–Seymour theorem, and in 2009 for his participation in the proof of the strong perfect graph theorem. He also won the Pólya Prize...

Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006). "The strong perfect graph theorem". Annals of Mathematics. 164: 51–229. arXiv:math/0212070. doi:10...

strong perfect graph theorem (with Neil Robertson, Paul Seymour, and Robin Thomas) characterizing perfect graphs as being exactly the graphs with no odd...

classes of perfect graphs from which all others can be formed in the proof by Chudnovsky et al. (2006) of the Strong Perfect Graph Theorem. If a graph is both...

According to the strong perfect graph theorem, induced cycles and their complements play a critical role in the characterization of perfect graphs. Cliques and...

especially graph theory. He (with others) was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless...

theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components...

analysis) Strong perfect graph theorem (graph theory) Symmetric hypergraph theorem (graph theory) Szemerédi's theorem (combinatorics) Theorem on friends...

component of a decomposition of perfect graphs used to prove the strong perfect graph theorem, which characterizes all perfect graphs. The independence number...

(Avraham Trahtman, 2007) Robertson–Seymour theorem (Neil Robertson, Paul Seymour, 2004) Strong perfect graph conjecture (Maria Chudnovsky, Neil Robertson...

results and conjectures concerning graph coloring are the following: Four-color theorem Strong perfect graph theorem Erdős–Faber–Lovász conjecture Total...

on the Hadwiger conjecture, and in 2009 for the proof of the strong perfect graph theorem. In 2011, he was awarded the Karel Janeček Foundation Neuron...

triangle-free graphs are bull-free graphs, since every bull contains a triangle. The strong perfect graph theorem was proven for bull-free graphs long before...

Robin Thomas in work published in 2006 and now known as the strong perfect graph theorem. Games were a passion of Claude Berge throughout his life, whether...

In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0...

bipartite graphs. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching and the Tutte theorem provides...

together with several gigabytes of computer calculations. 2006 the strong perfect graph theorem, by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin...

is Dilworth's theorem; these facts, together with the perfect graph theorem can be used to prove Dilworth's theorem from Mirsky's theorem or vice versa...