Author

Jie Han

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Preprint Sep 2026

On $P_4$-intersecting families of graphs

Given a graph $F$, a family $\mathcal F$ of graphs on $[n]$ is \emph{$F$-intersecting} if $G\cap H$ contains a copy of $F$ for every $G,H\in\mathcal F$. We prove that there exists an absolute constant $\varepsilon>0$ such that every $P_4$-intersecting family $\mathcal F$ satisfies $|\mathcal F|\le\left(\frac12-\varepsi...

Jie Han, Bin Wang · 1 citation · ⚡1

Preprint Sep 2026

Optimally pseudorandom $K_4$-free graphs

We show that optimally pseudorandom $K_4$-free graphs of order $n$ and degree $d = \Theta(n^{4/5})$ exist by constructing a graph in the split Cayley hexagon, matching the known upper bound. This resolves the first open case for $K_k$-free graphs after $k=3$ for which Alon gave a tight construction in 1994. This has a...

Jie Han, F. Ihringer, H. Van Maldeghem · 0 citations