Author

Xin Cheng

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Preprint Sep 2026

Quantum Query Algorithms for the Constructive Diagonal Ramsey Theorem

The constructive diagonal Ramsey problem asks, given adjacency-oracle access to an $N$-vertex graph, for a clique or independent set of the order guaranteed by Ramsey's theorem. We give a bounded-error quantum algorithm that, for every $K\ge2$ and $N\ge4^{K-1}$, finds and verifies a homogeneous $K$-set using $O\!\left(...

Xin Cheng · 0 citations

Preprint Sep 2026

On the Tur\'an number of the expansion of the book

The book with $t$ pages is the graph on $t+2$ vertices consisting of $t$ triangles which intersect at exactly one common edge. For a given graph $F$, the $r$-expansion $F^r$ of $F$ is the $r$-uniform hypergraph obtained from $F$ by adding $r-2$ distinct new vertices to each edge of $F$. We determine the Tur\'an number...

Xin Cheng, Dániel Gerbner, Hilal Hama Karim · 0 citations