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arXiv · 2601.19068

The linear Turán number of the 3-graph $P_5$

Chaoliang Tang·Hehui Wu·Junchi Zhang
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Abstract

We prove that for any linear 3-graph on $n$ vertices without a path of length 5, the number of edges is at most $\frac{15}{11}n$, and the equality holds if and only if the graph is the disjoint union of $G_0$, a graph with 11 vertices and 15 edges. Thus, $ex_L(n,P_5)\leq \frac{15}{11}n$, and the equality holds if and only if $11|n$.

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Chaoliang Tang, Hehui Wu, Junchi Zhang. 2026-01-27. The linear Turán number of the 3-graph $P_5$. https://arxiv.org/abs/2601.19068

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