2026/07/20 by Yinchen Liu, Quanyu Tang, Shengtong Zhang · 1 citation
#math.CO
Let G be an n-vertex graph with clique number ω(G), and let s+(G) denote the sum of the squared positive adjacency eigenvalues. We prove that √(s+(G))≤(1-(1)/(ω(G)))n. This strengthens Wilf's classical spectral Turán theorem and resolves a conjecture of Elphick and Wocjan. Adopting the relaxation of our companion paper on the square-energy conjecture, we reduce the theorem to a Motzkin--Straus inequality for doubly nonnegative matrices, which we prove via a local inverse-probability estimate for the Caro--Wei greedy algorithm on the complement.