Author

A. Gupta

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Preprint Aug 2026

A rate for the average vacancy of uniformly random matchings in linear hypergraphs

Let $M$ be chosen uniformly from all matchings of a finite linear $k$-uniform hypergraph $H$, and let $\overline{q}(H)$ be the average probability that a vertex is left uncovered. If $H$ has maximum degree $D$ and normalized average degree $\beta=k|E(H)|/(|V(H)|D)$, then, for every fixed $k\geq 2$ and uniformly in the...

A. Gupta · 0 citations

Preprint Aug 2026

Tuza's conjecture for graphs of maximum degree at most seven

Tuza conjectured that every finite simple graph $G$ satisfies $\tau(G) \leq 2\nu(G)$, where $\nu(G)$ is the maximum number of pairwise edge-disjoint triangles and $\tau(G)$ is the minimum number of edges whose deletion makes $G$ triangle-free. Puleo proved the conjecture for every graph of maximum average degree less t...

A. Gupta · 0 citations

Preprint Aug 2026

Edges of the uniform random forest of $K_n$ are pairwise negatively correlated for every $n$

Let $F_n$ be uniform on all forests of the simple complete graph $K_n$, with isolated vertices allowed. A conjecture of Kahn and of Winkler, studied by Grimmett and Winkler, asserts that any two distinct edges of any finite graph are negatively correlated under the uniform forest measure. Stark proved this for $G=K_n$...

A. Gupta · 0 citations

Preprint Aug 2026

Pairwise edge correlations in random minimum spanning trees: a universal bound and complete-graph negative correlation

Let $G$ be a finite connected multigraph whose edges receive independent weights from one atomless law, and let $\operatorname{MST}(G)$ be the resulting random minimum spanning tree. Its law is not pairwise negatively correlated: Lyons, Peres and Schramm exhibited two positively correlated edges, and we give such an ex...

A. Gupta · 2 citations · ⚡1