Current research interests:

Combinatorics and graph theory with emphasis on extremal problems for discrete structures (with special interests in finite partially ordered sets), on-line algorithms, approximation algorithms, ramsey theory, discrete geometry, and discrete optimization.

Current Research Problems:

1. Correlation Inequalities
2. Hamiltonian cycle and path problems
3. The Removable Pair Conjecture
4. The "1/3-2/3" Conjecture
5. Geometric Inclusion Orders
6. Distances in the Euclidean Plane
7. On-Line Graph Coloring
8. On-Line Chain Partitioning
9. The Dimension of Cartesian Products