Dr. Kains is interested primarily in connectivity of graphs. The intersection of longest cycles in k-connected graphs has been studied extensively, with results having significant implications in cybersecurity. Dr. Kains’ research explores results of long cycles in k-connected graphs that are not necessarily longest in the graph overall. He is interested in path analogues for these problems as well. Additionally, Dr. Kains is interested in scheduling problems, discrete math games, and statistical modeling. He is currently working on a predictive model for baseball results and is exploring the use of machine learning in brute force solutions for graph theory.