It is about a year old but still reflect my research interests. I will occasionally post updated versions. It is written in a somewhat informal manner. Some combinatorial questions Here are some of my current research interests and favorite problems. A feedback arc set in a digraph is a set of arcs whose removal makes the digraph acyclic.
Every acyclic digraph is a feedback arc set of some tournament.
That is, given an acyclic digraph, which we think of as the inconsistencies from a ranking, what is the smallest size of a tournament in which the ranking procedure described above gives exactly those inconsistencies. This provides bounds for other acyclic digraphs. More recent results have been obtained with recent Lehigh PhD Darren Narayan. See his research page for more information. Powers of Hamiltonian Paths Label the vertices of a graph so as to maximize the minimum distance between non-adjacent vertices.