7 papers
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…
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 $$ \sqrt{s^+(G)}\le\left(1-\…
The positive and negative square-energy conjecture
Yinchen Liu, Quanyu Tang, Shengtong Zhang
Let and denote the sums of the squares of the positive and negative adjacency eigenvalues of a graph , respectively. We prove the conjecture of Elphick, Farber…
Path-Minimality for Positive -Energies, Laplacian-Type Spectra, and Line Graphs
Yinchen Liu, Quanyu Tang
We derive several applications of the path-minimality theorem for adjacency -energy proved in the companion paper. First, we prove the sharp inequality $$ \mathcal E_p^+(G)\ge \…
Adaptivity Gaps for Stochastic Probing with Subadditive Functions
Jian Li, Yinchen Liu, Yiran Zhang
In this paper, we study the stochastic probing problem under a general monotone norm objective. Given a ground set , each element has an independent nonnegative…
On the Positive and Negative -Energies of Graphs under Edge Addition
Quanyu Tang, Yinchen Liu, Wei Wang
In this paper, we introduce the concepts of positive and negative -energies of graphs and investigate their behavior under edge addition. Specifically, we generalize the classic…