Many years ago, my colleague Lazaros Kikas gave a short seminar on his doctoral dissertation, in which he found results for the "k-disjoint path problem" in the alternating group graph. He had proven that disjoint paths existed in these graphs, but had left as an unsolved problem the question of whether an alogorithm could be found to efficiently generate the paths. I found the problem interesting, and took it home to think about on a Friday afternoon.
The next thing I knew, it was Monday morning. I had hardly eaten and not slept a wink, lost in thought about the problem (this happens to me on occasion). But I held in my hands what ended up being about 90% of a solution to the problem. I showed Lazaros the next day, and he said "Hey that's really good. How's it feel to finally be a researcher?"
It felt great! And within weeks we had begun a graph theory research group on the UDM campus, and I had done my first research in pure mathematics. Since then, I've continued working in graph theory, with the occasional forays into other areas. Click below to explore my research in the following areas: