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arXiv · 2409.09400

Subdivisions and near-linear stable sets

Tung Nguyen·Alex Scott·Paul Seymour
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Abstract

We prove that for every complete graph $K_t$, all graphs $G$ with no induced subgraph isomorphic to a subdivision of $K_t$ have a stable subset of size at least $|G|/{\rm polylog}|G|$. This is close to best possible, because for $t\ge 7$, not all such graphs $G$ have a stable set of linear size, even if $G$ is triangle-free.

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Tung Nguyen, Alex Scott, Paul Seymour. 2025-03-25. Subdivisions and near-linear stable sets. https://arxiv.org/abs/2409.09400

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