List of Research Papers - Much thanks to my collaborators and peers.  My research has been supported by the Simons Foundation and internal awards at Sac State.    

    35.  Generalized sum-free sets and cycle saturated regular graphs, with David Davini, submitted.

   34. Upper and lower bounds on the size of Bkg sets, with Griffin Johnston and Michael Tait, Australasian Journal of Combinatorics, Vol 83(1) (2022), 129-140. 

    33. Regular saturated graphs and sum-free sets, Discrete Mathematics, Vol 345, Issue 1 (2022),  . 

    32. Regular Turan numbers of complete bipartite graphs, with Michael Tait, Discrete Mathematics, Vol 344, Issue 10 (2021), 
  
    31. Minimizing the number of complete bipartite graphs in a Ks-saturated graph, with Beka Ergemlidze, Abhishek Methuku, and Michael Tait, to appear in Discussiones Mathematicae Graph Theory.  

      30. Triangles in Ks-saturated graphs with minimum degree t, with Benjamin Cole, Albert Curry, and David Davini, Theory and Applicaitons of Graphs, Vol. 7, Issue 1, Article 2.  .
  
      29. C2k-saturated graphs with no short odd cycles, Graphs and Combinatorics, Vol 35 Issue 5 Sep 2019, 1023-1034.   

     28. Few T copies in H-saturated graphs, with Jürgen Kritschgau, Abhishek Methuku, and Mike Tait, Journal of Graph Theory, Vol 94, Issue 3 July 2020, 32-348. The supporting Mathematica notebook file can be downloaded here.

      27. The Anti-Ramsey Problem for the Sidon equation, with Vladislav Taranchuk, Discrete Mathematics, Vol 342, Issue 10 (2019), 2856-2866.  
   
      26. The Zarankiewicz problem in 3-partite graphs, with Mike Tait, Journal of Combinatorial Designs, Vol. 27 no. 6 (2019), 391-405.   

      25. Turan numbers for Berge-hypergraphs and related extremal problems, with Cory Palmer, Mike Tait, and Adam Zsolt Wagner, Discrete Mathematics, Vol 342, Issue 6 (2019), 1553-1563.
     
    24. A note on the number of edges in a Hamiltonian graph with no repeated cycle length, with Joey Lee, Australasian Journal of Combinatorics, Volume 69(2) (2017), 286-291.  Remark: On January 7, 2018, I discovered that the same construction we used in our paper had been used by Boros, Erdos, Furedi, and Yuster in 2001 (Covering Non-uniform Hypergraphs, J. Comb. Theory Series B) to prove a lower bound on a very similar problem.       

      23. Triangle-free induced subgraphs of polarity graphs, with Jared Loucks.  The only version of this note is posted on the arXiv. For some progress, see Triangle-free induced subgraphs of the unitary polarity graph (Sam Mattheus and Francesco Pavese - the arXiv version can be found here), and On the indepenence number of graphs related to a polarity (Mattheus, Pavese, and Leo Storme - arXiv version here).

      22. Planar polynomials and an extremal problem of Fischer and Matousek, with Rex W. Matthews and Robert Coulter, J. Combinatorial Theory Series B 128 (2018), 96-103.     

    21. Degenerate Turan problems for hereditary properties, with Mike Tait and Vladimir Nikiforov, Electronic Journal of Combinatorics 24 (2018) no. 4 #P4.39.  

    20. Induced Turan numbers, with Po-Shen Loh, Mike Tait, and Rodrigo M. Zhou, Combinatorics, Probability, and Computing, Volume 27, Issue 2 March 2018.  
 
    19. On r-uniform linear hypergraphs with no Berge K2t, Electronic Journal of Combinatorics 24 (2017) no. 4 #P4.34.

    18. Upper bounds on Bhg-sets with small h, Integers 16 (2016) #A83, 12pp.

    17. Independent sets in polarity graphs, with Mike Tait, SIAM J. Discrete Math. 30 (2016), no. 4, 2115-2129.

    16. A path Turan problem for infinite graphs, with Xing Peng, Discrete Mathematics, Vol 340, Issue 2 (2017), 181-191.  

    15. A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results, with Thang Pham, Mike Tait, and Le Anh Vinh, J. Combinatorial Theory Series A 147 (2017), 55-74.     

   14. Small dense subgraphs of polarity graphs and the extremal number for the 4-cycle, with Mike Tait, The Australasian Journal of Combinatorics, Vol 63 Part 1 (2015), p. 107.  

   13. On the chromatic number of the Erdos-Renyi orthogonal polarity graph, with Mike Tait and Xing Peng, Electronic Journal of Combinatorics 22 (2015) no. 2 #P2.21.  

   12. Orthogonal polarity graphs and Sidon sets, with Mike Tait, Journal of Graph Theory 82 (2016) no. 1, 103-116.

   11. Bounds for generalized Sidon sets, with Rafael Tesoro and Xing Peng, Discrete Mathematics, Vol 338, Issue 3 (2015), 183-190.

   10. A counterexample to sparse removal, with Jacques Verstraete, European Journal of Combinatorics, Vol 44 Part A (2015), 77-86.

    9. Sidon sets and graphs without 4-cycles, with Mike Tait, Journal of Combinatorics, Vol 5 (2014), Issue 2, 155-165.   

    8. k-fold Sidon sets, with Javier Cilleruelo, Electronic Journal of Combinatorics 21 (2014) no. 4, #12.  

      7. Infinite Turan problems for bipartite graphs, with Xing Peng, SIAM J. Discrete Math. 28 (2014), no. 2, 702-710.      
     
      6. Upper and lower bounds on B_k^+-sets, Integers 14 (2014) #A1, 27pp.   

      5. An ordered Turan Problem for bipartite graphs, Electronic Journal of Combinatorics 19(4) 2012, #43.

    4.  Covering complete r-graphs with spanning complete r-partite r-graphs, with Sebastian M. Cioabă, André Kündgen, and Vladislav V. Vysotsky; Combinatorics, Probability and Computing, 20 (2011) no. 4, 519-527.  
   
    3.  Star coloring planar graphs from small lists, with André Kündgen, Journal of Graph Theory 63 (2010) no. 4, 324-337.
   
    2.  Star coloring bipartite planar graphs, with H. Kierstead and André Kündgen, Journal of Graph Theory 60 (2009) no. 1, 1-10.
   
    1.  Star coloring high girth planar graphs, Electronic Journal of Combinatorics 15 (2008) no. 1, #124.    



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