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arXiv · 2610.41286

On the Turán number for the Cartesian product of an odd cycle and a tree

Ya-Hong Chen·Yong Lu·Quan Sun·Qi Wu·Long-Tu Yuan
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Abstract

Let $T$ be a fixed tree on at least two vertices. We determine the Turán number and all extremal graphs for the Cartesian product of an odd cycle $C_{2m+1}$ and $T$, for every fixed integer $m\ge1$ and all sufficiently large $n$, in terms of its decomposition family. Every extremal graph is the join of an independent set and an extremal graph for that family. The proof combines the Erdős--Sós theorem with weak stability and progressive induction.

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Ya-Hong Chen, Yong Lu, Quan Sun, Qi Wu, Long-Tu Yuan. 2026-10-30. On the Turán number for the Cartesian product of an odd cycle and a tree. https://arxiv.org/abs/2610.41286

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