In the study of combinatorial designs, I am interested in mainly Steiner triple system, BIBDs, difference sets and covering designs. I have worked on projects that involved enumeration of all non-isomorphic designs with certain parameters, studied whether certain combinatorial designs exists. I have also studied properties of certain classes of designs such as friendship 3-hypergraphs and Sperner partition systems.

In my study of graphs, I am mainly interested in studying combinatorial optimization problems such as vertex cover and matchings. I am interested in developing approximation algorithms for NP-Hard problems. I am also interested in hardness of approximation of various NP-Hard problems. Finally I am interested studying subclasses of NP-Hard problems for which the subclasses are polynomial-time solvable.

**Here are my (submitted, accepted and published) articles from 2006 to current.**

- Guarding orthogonal terrains, with S. Durocher and S. Mehrabi (2015). Submitted.

__Cycle-maximal triangle-free graphs__, with S. Durocher, D.S. Gunderson, M. Skala. Discrete Mathematics 338(2015), 274-290.

- A sharp lower bound on the number of hyperedges in a friendship 3-hypergraph, with G.H.J. van Rees. Australian Journal of Combinatorics 57(2013),73-78.
__Friendship 3-hypergraphs__, with G.H.J. van Rees, S. H. Seo, and N.M. Singhi. Discrete Mathematics 312 (2012), 1892-1899.__Sperner partition systems__, with Karen Meagher. Accepted to appear in Journal of Combinatorial Designs (Accepted on July 19, 2012 and published online August 16, 2012).__Combination labelings of graphs__. Applied Mathematics E-Notes, 12(2012), 158-168.__Cool-lex Order and k-ary Catalan Structures__with Stephane Durocher, Debajyoti Mondal, Frank Ruskey, and Aaron Williams. Journal of Discrete Algorithms, special issue of invited papers selected from the Twenty-Second International Workshop on Combinatorial Algorithms (IWOCA 2011). 16(2012), 287-307.__A note on the Pancylism of block intersection graphs of universal-friend friendship hypergraphs__. Journal of Combinatorial Mathematics and Combinatorial Computing, 83(2010) 65-75.__Antimagic labelings of power of cycles graphs__. Accepted to Ars Combinatoria (July.23, 2011)- Ranking and Loopless Generation of k-ary Dyck Words in Cool-lex Order, with S. Durocher, D. Mondal, and A. Williams. In proceedings of the Twenty-Second International Workshop on Combinatorial Algorithms (IWOCA 2011). Springer Lecture Notes in Computer Science, 7056(2011), 182-194. 2011.
__Savate-Beam Triple Systems for v=5 and v=6__, with D.W. Hein. Journal of Combinatorial Mathematics and Combinatorial Computing, 57(2011), 161-168.__The Stein_Lovasz Theorem and its Application to Some Combinatorial Arrays__, with D. Deng, Y. Zhang, G.H.J. van Rees. Journal of Combinatorial Mathematics and Combinatorial Computing, 77(2011), 17-32.__Maximum Leaf Spanning Trees for Grid Graphs__, with M. Toulouse. Journal of Combinatorial Mathematics and Combinatorial Computing, 73(2010) 181-193.__Degree sequence conditions for partial Steiner triple systems__, with M.S. Keranen, D.L. Kreher, W.H. Kocay. Bulletin of the ICA, 57(2009) 71-73.- A Multilevel Cooperative Tabu Search Algorithm for the Covering Design Problem, with C. Dai, M. Toulouse. Journal of Combinatorial Mathematics and Combinatorial Computing, 68(2009) 33-66.
__Mutually Nearly Orthogonal Latin Squares__, with G.H.J. van Rees. Journal of Combinatorial Mathematics and Combinatorial Computing, 62(2007) 13-24.- On 3-Hypergraphs with Equal Degree Sequences, with W.L.Kocay. Ars Combinatoria, 82(2007) 145-157.
- Constructions and Bounds for (m,3)-Splitting Systems. Discrete Mathematics, with D. Deng, D.R. Stinson, G.H.J. van Rees, R. Wei. 307(2007), 18-37.
__There is no (22,8,4) Block Design__, with R.T. Bilous, C.W.H. Lam, L.H. Thiel, G.H.J. van Rees,S.P. Radziszowski, W.H. Holzmann, H. Kharaghani. Journal of Combinatorial Designs, 15 (2007) 262-267.- Constructions of 2-Cover-Free Families and Related Separating Hash Families, with G.H.J. van Rees, R. Wei. Journal of Combinatorial Designs, 14(2006), 423-440.
- Variations of the Maximum Leaf Spanning Tree Problem for Bipartite Graphs, with M. Toulouse. Information Processing Letters, 97(2006),129-132.
- Covering Designs on 13 Blocks, with M. Greig, G.H.J. van Rees. Utilitas Math. 70(2006) 221-261.
- Some NP-Completeness Results on Partial Steiner Triple Systems and Parallel Classes, with M. Toulouse. Ars Combinatoria 80(2006) 45-51.
- A Cooperative Multilevel Tabu Search Algorithm for the Covering Design Problem, with C. Dai,M. Toulouse. LNCS 3871(2006), 119-130.
- Lotto Designs (pages 529-536), with G.H.J. van Rees. The CRC Handbook of Combinatorial Designs, 2nd Edition(2006)
- On {123,124,134}-free systems, with D.R. Stinson, G.H.J. van Rees and R. Wei. Congressus Numerantium , V183 (2006) 161-174.

Expository Writings

Expository Writings

Here are some of my writings on various CS/mathematics topics. Most of these are just explanations on known results that I am interested in.

**Interesting Links**

Here is an article by Erza Brown on various interpretations of a Steiner triple system of order 7.