细分和近线性稳定集合

arXiv - MATH - Combinatorics Pub Date : 2024-09-14 DOI:arxiv-2409.09400

Tung Nguyen, Alex Scott, Paul Seymour

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引用次数: 0

摘要

我们证明，对于每一个完整图 $K_t$，所有没有诱导子图与 $K_t$ 的细分图同构的图 $G$，都有一个大小至少为 $|G|/{\rm polylog}|G|$ 的稳定子集。这接近于最佳可能，因为对于 $t/ge6$，并非所有这样的图 $G$ 都有线性大小的稳定子集，即使 $G$ 是无三角的。

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Subdivisions and near-linear stable sets

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 $t\ge 6$, not all such graphs $G$ have a stable set of linear size, even if $G$ is triangle-free.

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arXiv - MATH - Combinatorics

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