5 papers · 1 filter
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…
The forb-flex method for odd coloring and proper conflict-free coloring of planar graphs
James Anderson, Herman Chau, Eun-Kyung Cho +6
We introduce a new tool useful for greedy coloring, which we call the forb-flex method, and apply it to odd coloring and proper conflict-free coloring of planar graphs. The odd chr…
Asymmetric Ramsey properties of randomly perturbed graphs
Emily Heath, Daniel McGinnis
In this note, we investigate for various pairs of graphs the question of how many random edges must be added to a dense graph to guarantee that any red-blue coloring of the…
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…
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…