Research

My research interests are in graphy theory and combinatorics. In particular, I am interested in problems dealing with degree sequences and extremal graph theory. Below is a list of publications and, below that, other activities.

Publications

  • Constructive Upper Bounds for Cycle Saturated Graphs of Minimum Size [pdf]
          with Ron Gould, Tomasz Luczak
           Electronic Journal of Combinatorics, Vol. 13, 2006, R29 - 19pp.

  • Graphic Sequences with a Realization Containing a Friendship Graph [pdf]
          with M. Ferrara, R. Gould
           Ars Combinatoria, Vol. 85 (2007), 161-171.

  • Minimum Degree and the Minimum Size of K^t_2-saturated graphs [pdf]
          with R. Gould
           Discrete Mathematics, 307 (2007) 9-10, 1108-1114.

  • A note on minimum K_{2,3}-saturated graphs [pdf]
          with Oleg Pikhurko
           Australasian Journal of Combinatorics 40 (2008), 211-215.
         
  • Degree Sum Conditions in Graph Pebbling [pdf]
          with undergraduate student Anna Blasiak
           Australasian Journal of Combinatorics 42 (2008), 83-90.
         
  • Graphic Sequences with a Realization Containing a Complete Multipartite Subgraph[pdf]
          with Guantao Chen, M.Ferrara, R. Gould
           Discrete Mathematics 308 (2008) 23, 5712-5721.

  • Graphic Sequences with a Realization Containing a Generalized Friendship Graph [pdf]
           with J.H. Yin, Gang Chen
           Discrete Mathematics 308 (2008) 24, 6226-6232.

  • Using Edge Exchanges to Prove the Erdos-Jacobson-Lehel Conjecture [pdf]       
          with M.Ferrara, Ron Gould
           Bulletin of the Institute of Combinatorics and its Applications 57 (2009), 73-80.

  • Potentially H-Bigraphic Sequences[pdf]
          with M. Ferrara, Mike Jacobson, Mark Siggers
           to appear in Discussiones Mathematicae Graph Theory

  • A Sharp Lower Bound for Potentially H-Graphic Degree Sequences[pdf]
          with M.Ferrara
           SIAM Journal on Discrete Mathematics, 23 (2009) 1, 517-526.

    Extended Abstract

  • An Erdos-Stone Type Conjecture for Graphic Sequences [pdf]
          with M.Ferrara
           Electronic Notes in Discrete Mathematics (Proceedings of 6th Czech-Slovak International Symposium, Prague, 2006), Volume 28 (2007), 131-135.
         

    Co-authors

    Anna Blasiak, Gang Chen, Guantao Chen, Mike Ferrara, Ron Gould, Mike Jacobson, Tomasz Luczak, Oleg Pikhurko , Mark Siggers, J.H. Yin

    Acknowledgements

    I am grateful to Middlebury College , the Mathematical Sciences Program at the National Security Agency, and the National Science Foundation, particularly the RUI program, for their support. I am grateful for past support from Vermont EPSCoR.

    Activities

    In September 2007, I was the local organizer for Discrete Mathematics Day of Northeast Conference.

    Here is a research statement.

    Talks

    Here is a list of available recent talks.