11 papers · 1 filter
Off-Diagonal Commonality of Graphs via Entropy
Natalie Behague, Natasha Morrison, Jonathan A. Noel
A graph is common if the limit as of the minimum density of monochromatic labelled copies of in an edge colouring of with red and blue is attained by a s…
Directed cycles with zero weight in
Shoham Letzter, Natasha Morrison
For a finite abelian group , define to be the minimum integer such that for every complete digraph on vertices and every map , there exists…
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…