Practical approximation schemes for maximum induced-subgraph problems on K 3,3-free or K 5-free graphs

Abstract

We show that for an integer k ≥ 2 and an n-vertex graph G without a K 3,3 (resp., K 5) minor, we can compute k induced subgraphs of G with treewidth ≤ 3k−4 (resp., ≤ 6k−7) in O(kn) (resp., O(kn+n 2)) time such that each vertex of G appears in exactly k − 1 of these subgraphs. This leads to practical polynomial-time approximation schemes for various maximum induced-subgraph problems on graphs without a K 3,3 or K 5 minor. The result extends a well-known result of Baker that there are practical polynomial-time approximation schemes for various maximum induced-subgraph problems on planar graphs.