8 citations · 27 across the 15 of their papers we have counts for
20 papers · 1 filter
Explicit Fractalizers: Prime-Order Paley Graphs and other Cayley Graphs
Aldo Kiem, Fan Wei
The inducibility problem asks for the maximum number of induced copies of a fixed graph among all graphs with a prescribed number of vertices. Inducibility has been an active area…
A Characterization for Spectral and Trace Positivity of Matrix Words
Frederik Garbe, Fan Wei
In this paper, we provide a complete structural characterization of which words in noncommuting matrix variables and their formal transposes universally evaluate to matrices with n…
The limit points of the top and bottom eigenvalues of regular graphs
Noga Alon, Fan Wei
We prove that for each the set of all limit points of the second largest eigenvalue of growing sequences of -regular graphs is . A similar argument s…
An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals
Jake Ruotolo, Kevin Wang, Fan Wei
Let be a multipartite graph with partition of . Let denote the edge density of the pair . An independent transversal is an in…
Undecidability of polynomial inequalities in weighted graph homomorphism densities
Grigoriy Blekherman, Annie Raymond, Fan Wei
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using th…
Common graphs with arbitrary chromatic number
Daniel Kral, Jan Volec, Fan Wei
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdos conjectured that th…
On the asymptotic confirmation of the Faudree-Lehel Conjecture for general graphs
Jakub Przybyło, Fan Wei
Given a simple graph , the {\it irregularity strength} of , denoted by , is the least positive integer such that there is a weight assignment on edges $f: E(G) \to…
Short proof of the asymptotic confirmation of the Faudree-Lehel Conjecture
Jakub Przybyło, Fan Wei
Given a simple graph , the {\it irregularity strength} of , denoted , is the least positive integer such that there is a weight assignment on edges $f: E(G) \to \{1…
Threshold Ramsey multiplicity for odd cycles
David Conlon, Jacob Fox, Benny Sudakov +1
The Ramsey number of a graph is the minimum such that any two-coloring of the edges of the complete graph contains a monochromatic copy of . The threshold R…
Irregular Subgraphs
Noga Alon, Fan Wei
We suggest two related conjectures dealing with the existence of spanning irregular subgraphs of graphs. The first asserts that any -regular graph on vertices contains a spa…
Threshold Ramsey multiplicity for paths and even cycles
David Conlon, Jacob Fox, Benny Sudakov +1
The Ramsey number of a graph is the minimum integer such that any two-coloring of the edges of the complete graph contains a monochromatic copy of . While t…
Non-bipartite k-common graphs
Daniel Kral, Jonathan A. Noel, Sergey Norin +2
A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected…
Phase Transition of Degeneracy in Minor-Closed Families
Chun-Hung Liu, Fan Wei
Given an infinite family of graphs and a monotone property , an (upper) threshold for and is a "fastest growing" function…
On the inducibility problem for random Cayley graphs of abelian groups with a few deleted vertices
Jacob Fox, Lisa Sauermann, Fan Wei
Given a -vertex graph and an integer , what are the -vertex graphs with the maximum number of induced copies of ? This question is closely related to the inducibili…
Finding Cliques in Social Networks: A New Distribution-Free Model
Jacob Fox, Tim Roughgarden, C. Seshadhri +2
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the propert…
Fast property testing and metrics for permutations
Jacob Fox, Fan Wei
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are -far from satisfying the property. There are now several gen…
On the number of cliques in graphs with a forbidden subdivision or immersion
Jacob Fox, Fan Wei
How many cliques can a graph on vertices have with a forbidden substructure? Extremal problems of this sort have been studied for a long time. This paper studies the maximum po…
On the number of cliques in graphs with a forbidden minor
Jacob Fox, Fan Wei
Reed and Wood and independently Norine, Seymour, Thomas, and Wollan proved that for each positive integer there is a constant such that every graph on vertices with…
Involutions on standard Young tableaux and divisors on metric graphs
Rohit Agrawal, Gregg Musiker, Vladimir Sotirov +1
We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva between the set of rectangular standard Young tableaux and the set of equivalence classes of chip conf…
The Weak Bruhat Order and Separable Permutations
Fan Wei
In this paper we consider the rank generating function of a separable permutation in the weak Bruhat order on the two intervals and , where $w_0 = n,…