Efficient Approximation Schemes for Maximization Problems onK3, 3-free orK5-free Graphs

Abstract

We show that for any integerk≥2 and anyn-vertex graphGwithout aK3,3(orK5) minor, one can computekinduced subgraphs ofGwith treewidth no more than 3k−4 (respectively, 6k−7) inO(kn) (respectively,O(kn+n2)) time such that each vertex ofGappears in exactlyk−1 of these subgraphs. This leads topracticalpolynomial-time approximation schemes for various maximum induced-subgraph problems on graphs without aK3,3(respectively,K5) minor. The result extends the well-known practical polynomial-time approximation schemes of Baker for various maximum induced-subgraph problems onplanargraphs.