Large Induced Subgraphs via Triangulations and CMSO

Fedor V. Fomin, Ioan Todinca, Yngve Villanger
2015 SIAM journal on computing (Print)  
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
more » ... cial cases contains various problems as a special subcase: * Partially supported by the ANR project AGAPE.
doi:10.1137/140964801 fatcat:zmhblcqudrb5ffkuwmtybcdfye