We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (\textsc{MWIS}) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for \textsc{MWIS} in graphs that exclude sCt as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.
@article{arxiv.2602.18317,
title = {QPTAS for MWIS and finding large sparse induced subgraphs in graphs with few independent long holes},
author = {Édouard Bonnet and Jadwiga Czyżewska and Tomáš Masařík and Marcin Pilipczuk and Paweł Rzążewski},
journal= {arXiv preprint arXiv:2602.18317},
year = {2026}
}