Perfect graph
In graph theory a perfect graph is a graph in which the chromatic number of every induced subgraph equals the order of the largest clique of that subgraph clique number. There are many different types of graph makers out there and it can be difficult to decide which one is right for you.
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By de nition perfect graphs are the graphs such that for every induced subgraph the minimum number of colors in a proper coloring and the maximum size of a clique coincide.
. The graphs with V f1ngand E. The most trivial class of graphs that are perfect are the edgeless graphs ie. De nition 1 Perfect Graphs A graph G VE is perfect if for all S V GS GS.
Berges Perfect Graph Conjecture. These graphs and all of their subgraphs have both chromatic number and clique. 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.
In this graph and each of its induced subgraphs the chromatic number equals the. A graph is perfect if and only if neither the graph nor its. In graph theory a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals the number of maximal cliques.
In any graph the. Here are a few tips to help you choose the perfect graph. In graph theory a perfect graph or a Berge graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.
The Paley graph of order 9 colored with three colors and showing a clique of three vertices. By de nition perfect graphs are the graphs such that for every induced subgraph the minimum number of colors in a proper coloring and the maximum size of a clique coincide. Note that the equality is required to hold for all induced subgraphs of G.
Perfect graphs were defined by Claude Berge in the 1960s. Every distance-hereditary graph is a perfect graph more specifically a perfectly orderable graph and a Meyniel graph. Perfect graphs include many.
A perfect graph is a graph in which for every induced subgraph the size of the maximum clique equals the minimum number of colors in a coloring of the graph. This video reviews the history of an important conjecture later proved that was made in 1961. Clique number of a graph.
They are important objects for graph theory linear programming and combinatorial optimization. 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.
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