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arXiv · 2605.29176

Tightness of a MaxCut Lower Bound via Vector Chromatic Number

Emanuel Juliano
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Abstract

Recently, Balla, Janzer, and Sudakov showed a lower bound on the MaxCut in terms of the vector chromatic number, recovering known results on the MaxCut of $H$-free graphs. In this note, we show that their bound is tight, providing a construction that achieves a value arbitrarily close to the optimal constant. This answers a question raised by Elphick. Our construction is a modification of the geometric graph used by Feige and Schechtman to establish the integrality gap for the Goemans--Williamson semidefinite relaxation of the MaxCut.

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BibTeXRIS

Emanuel Juliano. 2026-05-27. Tightness of a MaxCut Lower Bound via Vector Chromatic Number. https://arxiv.org/abs/2605.29176

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