Biplanar Crossing Numbers and Random Graphs
Arran Hamm
Winthrop University https://www.winthrop.edu/cas/faculty/default.aspx?id=37026 

Abstract 
Prime Labeling Graphs and Hypergraphs
Graph labeling problems date back to the beginning of Graph Theory itself (namely in the form of graph coloring). Roughly 40 years ago the notion of prime labeling graphs was introduced; a graph on n vertices has a prime labeling if its vertices can be labeled by the numbers 1, 2,… , n so that each edge spans a coprime pair (with an analogous definition for prime labeling a hypergraph). Thus the problem: given a graph or hypergraph, is there a prime labeling? Our work focuses on a specific family of trees and a specific family of hypergraphs. In the former case, we give prime labelings and in the latter, we show that most members of the family are not prime. Joint work with Justin McCullough and Alan Way. 