collaborators

19 papers

math.CO2026

The -Conjecture for CIS -Graphs

Yinchen Liu, Quanyu Tang

We prove the -conjecture, which dates back to Gurvich's 1978 thesis. Specifically, let the edges of a complete graph be colored with colors , and for each let $G…

math.CO2026

Graph Eigenvalues and Projection Constants

Varun Sivashankar, Quanyu Tang, Tanay Wakhare

For an integer , let denote the th largest adjacency eigenvalue of a graph . For every graph on vertices and every , we prove \[ λ_…

math.NT2026

Integral Representations and Asymptotics for a Family of Areal Mahler Measures

Quanyu Tang, Shu Zhang

We answer a problem posed by Matilde Lalín concerning the areal Mahler measures of the multivariable polynomial family $$ P_n(x_1,\ldots,x_n,u) = \prod_{j=1}^n(1+x_j) + u\prod_{j=…

math.CO2026

A positive square-energy strengthening of Turán's theorem

Yinchen Liu, Quanyu Tang, Shengtong Zhang

Let be an -vertex graph with clique number , and let denote the sum of the squared positive adjacency eigenvalues. We prove that $$ \sqrt{s^+(G)}\le\left(1-\…

math.CO2026

The positive and negative square-energy conjecture

Yinchen Liu, Quanyu Tang, Shengtong Zhang

Let and denote the sums of the squares of the positive and negative adjacency eigenvalues of a graph , respectively. We prove the conjecture of Elphick, Farber…

math.CO2026

Minimum-rank parameters of complements of threshold Kneser graphs

Tao Hu, Quanyu Tang

Let be the graph whose vertices are the -subsets of , with two distinct vertices adjacent whenever their intersection has size at least . Equivalently,…