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arXiv · 2507.22509

A quasi-optimal upper bound for induced paths in sparse graphs

Basile Couëtoux·Oscar Defrain·Jean-Florent Raymond
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Abstract

In 2012, Nešetřil and Ossona de Mendez proved that graphs of bounded degeneracy that have a path of order $n$ also have an induced path of order $Ω(\log \log n)$. In this paper we give an almost matching upper bound by describing, for arbitrarily large values of $n$, 2-degenerate graphs that have a path of order $n$ and where the longest induced paths have order $O((\log \log n)^{1+o(1)})$.

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Basile Couëtoux, Oscar Defrain, Jean-Florent Raymond. 2026-02-12. A quasi-optimal upper bound for induced paths in sparse graphs. https://arxiv.org/abs/2507.22509

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