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arXiv · 2603.08675

The Lovász conjecture holds for moderately dense Cayley graphs

Benjamin Bedert·Nemanja Draganić·Alp Müyesser·Matías Pavez-Signé
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Abstract

We show that there is an absolute constant $c>0$ such that every large connected $n$-vertex Cayley graph with degree $d\geq n^{1-c}$ has a Hamilton cycle. This makes progress towards the Lovász conjecture and improves upon the previous best result of this form due to Christofides, Hladký, and Máthé from 2014 concerning graphs with $d\geq \varepsilon n$. Our proof avoids the use of Szemerédi's regularity lemma and relies instead on an efficient arithmetic regularity lemma specialised to Cayley graphs.

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Benjamin Bedert, Nemanja Draganić, Alp Müyesser, Matías Pavez-Signé. 2026-04-20. The Lovász conjecture holds for moderately dense Cayley graphs. https://arxiv.org/abs/2603.08675

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