2 citations · 10 across the 12 of their papers we have counts for
13 papers
Generalized Ramsey numbers of cycles, paths, and hypergraphs
Deepak Bal, Patrick Bennett, Emily Heath +1
Given a -uniform hypergraph and a set of -uniform hypergraphs , the generalized Ramsey number is the minimum number of colors needed to…
Edge-coloring a graph so that every copy of a graph has an odd color class
Patrick Bennett, Emily Heath, Shira Zerbib
Recently, Alon introduced the notion of an -code for a graph : a collection of graphs on vertex set is an -code if it contains no two members whose symmetric differe…
New bounds on the generalized Ramsey number
Enrique Gomez-Leos, Emily Heath, Alex Parker +2
Let denote the minimum number of colors needed to color the edges of so that every copy of receives at least distinct colors. In this note, we show $\fra…
The maximum number of odd cycles in a planar graph
Emily Heath, Ryan R. Martin, Chris Wells
How many copies of a fixed odd cycle, , can a planar graph contain? We answer this question asymptotically for and prove a bound which is tight up to a fa…
Embedded graph 3-coloring and flows
Caroline Bang, Zdeněk Dvořák, Emily Heath +1
A graph drawn in a surface is a near-quadrangulation if the sum of the lengths of the faces different from 4-faces is bounded by a fixed constant. We leverage duality between color…
Online Ramsey numbers of ordered paths and cycles
Felix Christian Clemen, Emily Heath, Mikhail Lavrov
An ordered graph is a graph with a linear ordering on its vertices. The online Ramsey game for ordered graphs and is played on an infinite sequence of vertices; on each tur…
Lower bounds on the Erdős-Gyárfás problem via color energy graphs
József Balogh, Sean English, Emily Heath +1
Given positive integers and , a -coloring of the complete graph is an edge-coloring in which every -clique receives at least colors. Erdős and Shelah pos…
Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response
Song Feng, Emily Heath, Brett Jefferson +25
Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular d…
Generalized rainbow Turán numbers of odd cycles
József Balogh, Michelle Delcourt, Emily Heath +1
Given graphs and , the generalized rainbow Turán number is the maximum number of copies of in an -vertex graph with a proper edge-co…
New Upper Bounds for the Erdős-Gyárfás Problem on Generalized Ramsey Numbers
Alex Cameron, Emily Heath
A -coloring of a graph is an edge-coloring of which assigns at least colors to each -clique. The problem of determining the minimum number of colors, $f(n,p,q…
A Strengthening of the Erdős-Szekeres Theorem
József Balogh, Felix Christian Clemen, Emily Heath +1
The Erdős-Szekeres Theorem stated in terms of graphs says that any red-blue coloring of the edges of the ordered complete graph contains a red copy of the monotone incre…
Ordered Size Ramsey Number of Paths
József Balogh, Felix Christian Clemen, Emily Heath +1
An ordered graph is a simple graph with an ordering on its vertices. Define the ordered path to be the monotone increasing path with edges. The ordered size Ramsey number…
A -coloring of with few colors
Alex Cameron, Emily Heath
For fixed integers and , let denote the minimum number of colors needed to color all of the edges of the complete graph such that no clique of vertices…