[PDF][PDF] Explicit two-sided unique-neighbor expanders

JT Hsieh, T McKenzie, S Mohanty… - Proceedings of the 56th …, 2024 - dl.acm.org
We study the problem of constructing explicit sparse graphs that exhibit strong vertex
expansion. Our main result is the first two-sided construction of imbalanced unique-neighbor …

Arbitrary Spectral Edge of Regular Graphs

D Dong, T McKenzie - arXiv preprint arXiv:2412.09570, 2024 - arxiv.org
We prove that for each $ d\geq 3$ and $ k\geq 2$, the set of limit points of the first $ k $
eigenvalues of sequences of $ d $-regular graphs is\[\{(\mu_1,\dots,\mu_k) …

Unique-neighbor Expanders with Better Expansion for

Y Chen - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
Abstract A (d 1 d 2)-biregular bipartite graph G=(L∪ R, E) is called left-(m, δ) unique-
neighbor expander iff each subset S of the left vertices with| S|≤ m has at least δd 1| S …

Combinatorics via closed orbits: Number theoretic Ramanujan graphs are not unique neighbor expanders

A Kamber, T Kaufman - Proceedings of the 54th Annual ACM SIGACT …, 2022 - dl.acm.org
The question of finding expander graphs with strong vertex expansion properties such as
unique neighbor expansion and lossless expansion is central to computer science. A barrier …

A combinatorial approach to nonlinear spectral gaps

DJ Altschuler, P Dodos, K Tikhomirov… - arXiv preprint arXiv …, 2024 - arxiv.org
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular
graph which satisfies the classical discrete Poincar\'e inequality for scalar functions, also …

Unique-neighbor Expanders with Better Expansion for Polynomial-sized Sets

Y Chen - arXiv preprint arXiv:2410.07061, 2024 - arxiv.org
A $(d_1, d_2) $-biregular bipartite graph $ G=(L\cup R, E) $ is called left-$(m,\delta) $
unique-neighbor expander iff each subset $ S $ of the left vertices with $| S|\leq m $ has at …

[PDF][PDF] On the Expansion of Graphs

P Paredes - 2022 - cs.princeton.edu
A popular way of analyzing a graph is through spectral properties of its associated matrices,
such as the adjacency matrix or the Laplacian matrix. This type of analysis has produced …

Random Walks and Delocalization through Graph Eigenvector Structure

TR McKenzie - 2022 - search.proquest.com
Discrete graphs are ubiquitous models applicable to many areas, useful for any discrete
system with some notion of connectivity. Some examples for which these are useful are …

The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph

T McKenzie - Comptes Rendus. Mathématique, 2022 - numdam.org
Anantharaman and Le Masson proved that any family of eigenbases of the adjacency
operators of a family of graphs is quantum ergodic (a form of delocalization) assuming the …

[PDF][PDF] MASTERARBEIT

G Ehling - 2022 - phaidra.univie.ac.at
MASTERARBEIT / MASTER’S THESIS Page 1 MASTERARBEIT / MASTER’S THESIS Titel der
Masterarbeit / Title of the Master’s Thesis Margulis’ Expanders and Ramanujan Graphs …