Research

My research interests are in graphy theory and combinatorics. In particular, my main interests are in extremal graph theory. I particularly like questions that are of the following form: "How small can a discrete structure be while still maintaining a particular desired property?" Below is a list of publications and, below that, other activities.

Submissions/To appear


  1. Martin Gardner's minimum no-three-in-a-line problem [pdf]
          with undergraduate student Alec Cooper, Oleg Pikhurko and Greg Warrington
           American Mathematical Monthly, to appear
           (And, see the On-line Encyclopedia of Integer Sequences entry A219760.)

    Publications


  2. On the size and structure of graphs with a constant number of 1-factors [pdf]
          with Andrzej Dudek
           Discrete Mathematics 312 (2012), 1807-1811

  3. Saturation numbers for families of ramsey-minimal graphs [pdf]
          with Guantao Chen, M.Ferrara, R. Gould, and C. Magnant
           Journal of Combinatorics 2 (2011), 435-456.

  4. A Survey of Minimum Saturated Graphs [pdf]
          with J. Faudree, R. Faudree
           Electronic Journal of Combinatorics Dynamic Survey 18 (2011), #DS19 36pp.

  5. A Sharp Lower Bound for Potentially H-Graphic Degree Sequences[pdf]
    (Slightly revised from published version thanks to comments from Vera Sos.)
          with M.Ferrara
           SIAM Journal on Discrete Mathematics 23 (2009) 1, 517-526.

  6. Potentially H-Bigraphic Sequences[pdf]
          with M. Ferrara, Mike Jacobson, Mark Siggers
           Discussiones Mathematicae Graph Theory 29 (2009) 583-596.

  7. 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.

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

  9. 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.

  10. Degree Sum Conditions in Graph Pebbling [pdf]
          with undergraduate student Anna Blasiak
           Australasian Journal of Combinatorics 42 (2008), 83-90.
         
  11. A note on minimum K_{2,3}-saturated graphs [pdf]
          with Oleg Pikhurko
           Australasian Journal of Combinatorics 40 (2008), 211-215.
         
  12. Minimum Degree and the Minimum Size of K^t_2-saturated graphs [pdf]
          with R. Gould
           Discrete Mathematics 307 (2007) 9-10, 1108-1114.

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

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




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, Alec Cooper, Gang Chen, Guantao Chen, Andrzej Dudek, Jill Faudree, Ralph Faudree, Mike Ferrara, Ron Gould, Mike Jacobson, Tomasz Luczak, Colton Magnant, Oleg Pikhurko , Mark Siggers, J.H. Yin, Greg Warrington

    Acknowledgements

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

    Activities

    I am the local organizer for Discrete Mathematics Day of Northeast Conference, to be held September 15, 2012. In September 2007, I was the local organizer for Discrete Mathematics Day of Northeast Conference.

    In the past, I served (2010-2011) as Secretary of Society of Industrial and Applied Mathematics' Activity Group on Discrete Mathematics.

    Talks

    Here is a list of available recent talks.