9 papers
The Typical Structure of Sets with Small Sumset
Marcelo Campos, Maurício Collares, Robert Morris +2
In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we…
Bounding the number of cycles in a graph in terms of its degree sequence
Zdeněk Dvořák, Natasha Morrison, Jonathan A. Noel +2
We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Király and Arman and Tsatur…
Lagrangians of Hypergraphs II: When colex is best
Vytautas Gruslys, Shoham Letzter, Natasha Morrison
A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of colex of has the largest Lagrangian of any -uniform hypergraph with hyperedges. We s…
The Kőnig Graph Process
Nina Kamčev, Michael Krivelevich, Natasha Morrison +1
Say that a graph G has property if the size of its maximum matching is equal to the order of a minimal vertex cover. We study the following process. Set $N:= \binom{n…
On the singularity of random symmetric matrices
Marcelo Campos, Letícia Mattos, Robert Morris +1
A well-known conjecture states that a random symmetric matrix with entries in is singular with probability . In this paper we prove…
Maximising the Number of Cycles in Graphs with Forbidden Subgraphs
Natasha Morrison, Alexander Roberts, Alex Scott
Fix and let be a graph with containing a critical edge. We show that for sufficiently large , the unique -vertex -free graph containing the maxi…