I have considered some extremal problems of the following type. Given a family of subsets of a set of size n where the family satisfies certain specified properties, determine the maximum possible number of subsets in the family as a function of n . For certain specified properties, exact best possible bounds have been obtained and sometimes the structure of families achieving the bounds are elucidated. In other cases asymptotically best possible bounds are obtained. A great many combinatorial structures have forbidden substructures and the results above find application in other combinatorial problems.
Graph theory is a central area in combinatorics.
A variety of problems are considered such as examining the structure of certain classes of graphs. With Martin Farber results were obtained concerning the class of bridged graphs. These are graphs which contain no cycle of length greater than three as an isometric subgraph. With J. Pryzytcki and D. Rolfsen, results of Tutte on rotors in graphs and chromatic polynomials were extended to mutations of knots and knot polynominals. Recent work has found fast algorithms for determining diameter critical graphs.