Large Induced Subgraphs via Triangulations and CMSO

@inproceedings{Fomin2015LargeIS,
  title={Large Induced Subgraphs via Triangulations and CMSO},
  author={F. Fomin and Ioan Todinca and Yngve Villanger},
  booktitle={SIAM J. Comput.},
  year={2015}
}
We obtain an algorithmic metatheorem for the following optimization problem. Let $\varphi$ be a counting monadic second order logic (CMSO) formula and $t\geq 0$ be an integer. For a given graph $G=(V,E)$, the task is to maximize $|X|$ subject to the following: there is a set $ F\subseteq V$ such that $X\subseteq F $, the subgraph $G[F]$ induced by $F$ is of treewidth at most $t$, and the structure $(G[F],X)$ models $\varphi$, i.e., $(G[F],X)\models\varphi$. We give an algorithm solving this… 

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