Author

F. Ihringer

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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 · 2 citations

Preprint Aug 2026

An improved algebraic construction for Ramsey numbers

We provide an explicit algebraic construction showing that, uniformly for integers $3 \leq s \leq t$, as $t \to \infty$, \[ R( s,t ) \geq t^{(1-o(1)) \log s / \log(\log s + 1) }. \] For large fixed $s$, this improves the dependence on $s$ in the general off-diagonal construction of Alon and Pudl\'ak. In particular, $R(...

F. Ihringer, Sam Mattheus · 3 citations · ⚡1