Estes is a graph theorist with a background in independence, including independence polynomials, backbone colorings, maximal outerplanar graphs, and a generalization of trees known as k-trees. In particular, he has investigated extremal cases of k-trees with regard to many metrics, including Zagreb indices. More recently, he and his students have investigated random walks through Markov chains on graphs, in particular, random walks with absorbing states. He is also interested in investigating machine learning and artificial intelligence, looking at algorithmic graph searches and supervised learning techniques.