Vishesh Jain

activity

20222026

most citedDimension reduction for maximum matchings and the Fastest Mixing Markov Chain

1 citations · 1 across the 18 of their papers we have counts for

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6 papers · 1 filter

math.CO2026

Optimal girth-dependent bounds for the Bethe approximation of the permanent

Dingding Dong, Vishesh Jain

For an $n \times n$ nonnegative matrix $A$ , the Bethe permanent, which is computable in deterministic polynomial time, satisfies the tight universal comparison \[\operatorname{Bethe…

math.CO2026

On the maximum density of $r$ -graphs in which every $(r + 1)$ -set spans $0$ or $2$ edges

Vishesh Jain, Haoran Luo, Dhruv Mubayi

In 1984, Frankl and Füredi asked for the maximum density of an $n$ -vertex $r$ -graph in which every $(r + 1)$ -set of vertices spans $0$ or $2$ edges. They gave a construction with asy…

math.CO2026

The size of the spanning-tree spectrum of simple graphs

Vishesh Jain

For a graph $G$ , let $τ (G)$ denote the number of spanning trees. We show that for every fixed $0 < c < 1/4$ , the number of distinct values of $τ (G)$ , as $G$ ranges over simple grap…

math.CO2026

Equality in Fill's spectral gap problem

Vishesh Jain, Clayton Mizgerd

We study the adjacent-transposition chain on the symmetric group $S_{n}$ with a regular parameter vector $p = (p_{i, j})_{i \neq = j}$ . Fill's spectral gap conjecture, r…

math.CO2025

The random graph process is globally synchronizing

Vishesh Jain, Clayton Mizgerd, Mehtaab Sawhney

The homogeneous Kuramoto model on a graph $G = (V, E)$ is a network of $∣ V ∣$ identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit…

math.CO2024

An explicit economical additive basis

Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1

We present an explicit subset $A \subseteq N = {0, 1, \dots}$ such that $A + A = N$ and for all $ε > 0$ , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…

Optimal girth-dependent bounds for the Bethe approximation of the permanent

On the maximum density of r-graphs in which every (r+1)-set spans 0 or 2 edges

The size of the spanning-tree spectrum of simple graphs

Equality in Fill's spectral gap problem

The random graph process is globally synchronizing

An explicit economical additive basis

On the maximum density of $r$ -graphs in which every $(r + 1)$ -set spans $0$ or $2$ edges