QPTAS for Max Weight Independent Set in Graphs with Strongly Edge-Sublinear Separators
Abstract
A hereditary graph class has strongly edge-sublinear separators if, for some constant 0 leqslant b < 1, every graph in the class with m edges admits a balanced separator of size 𝒪(mb). We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding particular induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].
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BibTeX
@misc{bonnet2026qptas,
title = {{QPTAS for Max Weight Independent Set in Graphs with Strongly Edge-Sublinear Separators}},
author = {Édouard Bonnet and Yeonsu Chang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16025},
eprint = {2610.16025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16025},
}
RIS
TY - UNPB
TI - QPTAS for Max Weight Independent Set in Graphs with Strongly Edge-Sublinear Separators
AU - Édouard Bonnet
AU - Yeonsu Chang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16025
UR - https://arxiv.org/abs/2610.16025
AB - A hereditary graph class has strongly edge-sublinear separators if, for some constant 0 leqslant b < 1, every graph in the class with m edges admits a balanced separator of size 𝒪(m^b). We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding particular induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].
ER -