Thomas began independent research after succeeding in a graph theory course and thereby recommended to start research with a professor specializing in graph theory.

Thomas studies Hadwiger’s Conjecture, which claims that all graphs have certain properties which guarantee the existence of smaller sub-structures. Having gone unsolved for decades, a new direction with Hadwiger’s Conjecture is to consider a more difficult version which claims the existence of sub-structures called dominating clique minors. Thomas has studied the existing results for Hadwiger’s Conjecture and its “dominating” variant, while also using a novel method to prove that the dominating version is true for an interesting class of graphs called 2K2-free.

Thomas tells students: “If you take on an ambitious project, especially in mathematics, there will be many times when your problem seems intimidating and potentially impossible. You might find yourself frustrated by continually trying and failing to find a way around the barriers to your objective. When this happens, be persistent but don’t let yourself get trapped in tunnel vision. Many times, during my toughest weeks, the best thing I did was take a short break, ask my colleagues about their research, and give myself a moment to find a new angle on my own problems. Although you must be diligent and efficient, recognize that the ideas you need could truly come from anywhere. Research wouldn’t be fun if it were always straightforward.”