6 papers · 1 filter
Sharp Nordhaus-Gaddum bounds for throttling
Ryan Blair, Gabriel Elvin, Veronika Furst +2
Throttling is a graph optimization problem, where the throttling number of a graph is the minimum sum or minimum product of the number of vertices in an initial set and the time re…
Bounds on Arithmetic Rainbow Ramsey Multiplicities
Gabriel Elvin, Alexis Gonzales, Alejandro Rodriguez +1
We study a quantitative Ramsey-type problem on 3-term arithmetic progressions: how should the set of integers be colored using 3 colors in order to maxim…
On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three
Gabriel Elvin, Hajrudin Fejzić, Youngsu Kim
We provide a simplified proof of the following special case of Wegner's conjecture: every planar graph of maximum degree at most three admits a distance-2 coloring with at most eig…
Sharp bounds for product and sum throttling numbers
Ryan Blair, Gabriel Elvin, Veronika Furst +3
Throttling in graphs optimizes a sum or product of resources used, such as the number of vertices in an initial set, and time required, such as the propagation time, to complete a…
Bounds for Rainbow-uncommon Graphs
Blake Bates, Zhanar Berikkyzy, Nick Chiem +6
We say a graph is -rainbow-uncommon if the maximum number of rainbow copies of under an -coloring of is asymptotically (as ) greater than what…
Avoiding Monochromatic Solutions to 3-term Equations
Kevin P. Costello, Gabriel Elvin
Given an equation, the integers as inputs, and the colors red and blue, how can we color in order to minimize the number of monochromatic solutions…