3 Treewidth 13 3.1 Definition and basic properties . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Recursively defined graph classes . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Chordal graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Search games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Separators . . . . . . . ....

I study active learning in general pool-based active learning models as well noisy active learning algorithms and then compare them for the class of linear separators under the uniform distribution.

3 Treewidth 12 3.1 Definition and basic properties . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Recursively defined graph classes . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Chordal graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Search games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.5 Separators . . . . . . . ....

We show that graphs do not contain a theta, pyramid, prism, or turtle as an induced subgraph have polynomially many minimal separators. This result is the best possible in sense there are with exponentially separators if only three of four subgraphs excluded. As consequence, polynomial time algorithm to solve maximum weight independent set problem for class (theta, turtle)-free graphs. Since ev...