For what kind of graphs, finding maximum independent set is possible in polynomial time ?
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I am doing my thesis these days about "treewidth". This parameter is closely related with other parameters and with perfect graphs. "In all perfect graphs, the graph coloring problem, maximum clique problem, and maximum independent set problem can all be solved in polynomial time" (taken from wikipedia)" Some perfect graphs that I am familiar with are the "bipartite"(not odd cycles) graphs and the "chordal"(not induced cycle bigger than 3) graphs.
I hope you have free time