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Large Induced Subgraphs via Triangulations and CMSO

2015
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SIAM journal on computing (Print)
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We obtain an algorithmic meta-theorem for the following optimization problem. Let ϕ be a Counting Monadic Second Order Logic (CMSO) formula and t ≥ 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 ⊆ V such that X ⊆ F , the subgraph G[F ] induced by F is of treewidth at most t, and structure (G[F ], X) models ϕ, i.e. (G[F ], X) |= ϕ. Special cases of this optimization problem are the following generic examples. Each of these

doi:10.1137/140964801
fatcat:zmhblcqudrb5ffkuwmtybcdfye