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...

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

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...

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

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

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...

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...

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

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

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

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

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...

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

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

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...

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

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

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...

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...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

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

induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings...

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

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

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...

the strong perfect graph theorem, for the graphs that have no bull graph as an induced subgraph.[B] Their work in this area introduced a type of graph decomposition...