65 citations · 268 across the 20 of their papers we have counts for
16 papers · 1 filter
Bounds on median eigenvalues of graphs of bounded degree
Hricha Acharya, Zilin Jiang, Shengtong Zhang
We prove that for every integer , the median eigenvalues of any graph of maximum degree are bounded above by . We also prove that, in three separate cases,…
Forbidden induced subgraphs for graphs and signed graphs with eigenvalues bounded from below
Zilin Jiang, Alexandr Polyanskii
The smallest eigenvalue of a graph is the smallest eigenvalue of its adjacency matrix. We show that the family of graphs with smallest eigenvalue at least can be defined by a…
Rainbow odd cycles
Ron Aharoni, Joseph Briggs, Ron Holzman +1
We prove that every family of (not necessarily distinct) odd cycles in the complete graph on vertices has a rainbow odd cycle (that…
Negligible obstructions and Turán exponents
Tao Jiang, Zilin Jiang, Jie Ma
We show that for every rational number of the form , where satisfy …
Spherical two-distance sets and eigenvalues of signed graphs
Zilin Jiang, Jonathan Tidor, Yuan Yao +2
We study the problem of determining the maximum size of a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let denote th…
Equiangular lines with a fixed angle
Zilin Jiang, Jonathan Tidor, Yuan Yao +2
Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separat…
An isoperimetric inequality for Hamming balls and local expansion in hypercubes
Zilin Jiang, Amir Yehudayoff
We prove a vertex isoperimetric inequality for the -dimensional Hamming ball of radius . The isoperimetric inequality is sharp up to a constant factor for…
Cooperative colorings of trees and of bipartite graphs
Ron Aharoni, Eli Berger, Maria Chudnovsky +2
Given a system of graphs on the same vertex set , a cooperative coloring is a choice of vertex sets , such that is independent in $G…
Rainbow fractional matchings
Ron Aharoni, Ron Holzman, Zilin Jiang
We prove that any family of (not necessarily distinct) sets of edges in an -uniform hypergraph, each having a fractional matching of size $n…
On the metric dimension of Cartesian powers of a graph
Zilin Jiang, Nikita Polyanskii
A set of vertices resolves a graph if every vertex is uniquely determined by its vector of distances to the vertices in . The metric dimension of a graph is the minimum card…
On spectral radii of unraveled balls
Zilin Jiang
Given a graph , the unraveled ball of radius centered at a vertex is the ball of radius centered at in the universal cover of . We prove a lower bound on the…
Ramsey-nice families of graphs
Ron Aharoni, Noga Alon, Michal Amir +5
For a finite family of fixed graphs let be the smallest integer for which every -coloring of the edges of the complete graph yields a…
Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines
Zilin Jiang, Alexandr Polyanskii
The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let be the family of connected graphs of spectral radius . We show that $\…
Bipartite algebraic graphs without quadrilaterals
Boris Bukh, Zilin Jiang
Let be the -dimensional complex projective space, and let be two non-empty open subsets of in the Zariski topology. A hypersurface in $\…
A Slight Improvement to the Colored Bárány's Theorem
Zilin Jiang
Suppose absolutely continuous probability measures on are given. In this paper, we prove that there exists a point of that be…
A bound on the number of edges in graphs without an even cycle
Boris Bukh, Zilin Jiang
We show that, for each fixed , an -vertex graph not containing a cycle of length has at most edges.