Papers
(categories are approximations!)
Extremal graph theory
Small dense subgraphs of polarity graphs and the extremal number for the 4-cycle, Australasian Journal of Combinatorics, Volume 63 (1) (2015), 107--114, with Craig Timmons.
Degree Ramsey numbers of even cycles, Discrete Mathematics, 341(1) (2017), 104--108.
Induced Turán numbers, Combinatorics, Probability and Computing (2017), 1--15, with Po-Shen Loh, Craig Timmons, and Rodrigo Zhou.
Turán numbers for Berge-hypergraphs and related extremal problems, Discrete Mathematics 342 (6) (2019), 1553--1563, with Cory Palmer, Craig Timmons, and Adam Wagner.
The Zarankiewicz problem in 3-partite graphs, Journal of Combinatorial Designs 27(6) (2019), 391--405, with Craig Timmons
Turán number of theta graphs, Combinatorics, Probability and Computing, 29 (4), (2020), 495-507, with Boris Bukh.
Linearity of saturation for Berge hypergraphs, European Journal of Combinatorics, 78 (2019), 205--213. With Sean English, Dani Gerbner, and Abhi Methuku.
Hypergraphs with few Berge paths of fixed length between vertices, SIAM Journal on Discrete Math, 33 (3), (2019), 1472--1481 with Sunny He .
Few T copies in H-saturated graphs, Journal of Graph Theory, 94 (3), (2020), 320--348, with Juergen Kritschgau, Abhi Methuku, and Craig Timmons.
Large monochromatic components in 3-edge-colored Steiner triple systems, Journal of Combinatorial Designs 28 (6), (2020), 428--444, with Louis DeBiasio.
Turán and Ramsey-type results for unavoidable subgraphs, Journal of Graph Theory, 101 (4), (2022), 597--622, with Alp Müyesser.
Regular Turán numbers for complete bipartite graphs, Discrete Mathematics, 344 (10), 112531, (2021), with Craig Timmons.
On a colored Turán problem of Diwan and Mubayi, Discrete Mathematics 345(10), 113003 ,with Ander Lamaison and Alp Müyesser.
Minimizing the number of complete bipartite graphs in a $K_s$-saturated graph, Discussiones Mathematicae Graph Theory, 43 (3), (2023), 793--807. with Beka Ergemlidze, Abhi Methuku, and Craig Timmons.
Multicolor Ramsey numbers for Berge cycles, The Electronic Journal of Combinatorics, Volume 29, Issue 4 (2022), P4.26, with Zach DeStefano, Hannah Mahon, and Frank Simutis
Improved upper bounds on even-cycle creating Hamilton paths, Discrete Mathematics, 347 (10), 114107 (October 2024), with John Byrne
Forbidden subgraphs and complete partitions, to appear in Electronic Journal of Combinatorics, with John Byrne and Craig Timmons
Hypergraphs of girth 5 and 6 and coding theory, with Katie Haymaker and Craig Timmons
Decomposition family and spectral extremal problems on non-bipartite graphs, Discrete Mathematics, 348 (10), 114527 (October 2025), with Longfei Fang and Mingqing Zhai
Combinatorial number theory
Sidon sets and graphs without 4-cycles. Journal of Combinatorics, Volume 5, Number 2, 155--165 (2014), with Craig Timmons.
Orthogonal polarity graphs and Sidon sets, Journal of Graph Theory 82(1) (2016), 103--116, with Craig Timmons.
On sets of integers with restrictions on their products, European Journal of Combinatorics 51 (2016) 268--274, with Jacques Verstraete.
A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results, Journal of Combinatorial Theory, Series A, Volume 147 (2017), 55--74. With Thang Pham, Craig Timmons, and Le Anh Vinh.
A structure theorem for product sets in extra special groups, Journal of Number Theory, 184 (2018), 461--472, with Thang Pham, Le Anh Vinh, and Rob Won.
Rainbow number for $x_1 + x_2 = kx_3$ in $\mathbb{Z}_n$, Integers 20 (2020), 2, with Erin Bevilacqua, Sam King, Juergen Kritschgau, Suzannah Tebon, and Michael Young.
Sidon sets and 2-caps in $\mathbb{F}_3^n$, Involve, 12 (6) (2019), 995--1003, with Alice Huang and Rob Won.
Improved lower bound for difference bases, Journal of Number Theory, 205 (2019), 50--58, with Anton Bernshteyn.
Improved bounds on the sizes of generalized caps in AG(n,q), SIAM Journal on Discrete Math 35 (1), (2021), 521--531, with Robert Won.
Upper and lower bounds on the size of $B_k[g]$ sets, Australasian Journal of Combinatorics, 83 (1), (2022), 129--140, with Griffin Johnston and Craig Timmons
An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory, European Journal of Combinatorics 118, 103928, 2024, with Alex Iosevich, Thang Pham, and Steven Senger
Cardinalities of g-difference sets, to appear in Integers, with Eric Schmutz
Improved bounds on the postage stamp problem for large numbers of stamps, with Eric Faust
Spectral graph theory
Degenerate Turán problems for hereditary properties, The Electronic Journal of Combinatorics, 25(4), P4.39, (2018), with Vlado Nikiforov and Craig Timmons.
Spectral bounds for the k-independence number of a graph, Linear Algebra and its Applications, 510 (2016), 160--170, with Aida Abiad and Sebastian Cioaba.
On the distance spectra of graphs. Linear Algebra and its Applications, Volume 497, (2016), 66--87, with 11 authors.
Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree, Electronic Journal of Linear Algebra, 34.27, (2018), 373--380, with Ghodrat Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin Kenter, and Jephian Lin.
Characterizing graphs of maximum principal ratio, Electronic Journal of Linear Algebra, 34.1 (2018), 61--70, with Josh Tobin.
Three conjectures in extremal spectral graph theory, Journal of Combinatorial Theory, Series B, 126 (2017), 137--161, with Josh Tobin.
The Colin de Verdiere Parameter, excluded minors, and the spectral radius, Journal of Combinatorial Theory Series A, Volume 166 (2019), 42--58.
The maximum relaxation time of a random walk, Advances in Applied Mathematics, Volume 101 (2018), 1--14, with Sinan Aksoy, Fan Chung, and Josh Tobin.
The maximum spectral radius of graphs without friendship subgraphs, Electronic Journal of Combinatorics P4.22 (2020) with Sebi Cioaba, Lihua Feng, and Xiao-Dong Zhang.
The spectral radius of graphs with no odd wheels, European Journal of Combinatorics 99, 103420, with Sebi Cioaba and Dheer Noal Desai
Spectral extremal graphs for intersecting cliques, Linear Algebra and its Applications, Volume 644, 1 (2022), 234--258, with Dheer Noal Desai, Liying Kang, Yongtao Li, Zhenyu Ni, and Jing Wang
On the maximum spread of graphs and bipartite graphs, Communications of the AMS, 2 (2022), 417--480, with Jane Breen, Alex Riasanovsky, and John Urschel
On the spread of outerplanar graphs, Special Matrices 10 (1), (2022), 299--307, with Daniel Gotshall and Megan O'Brien
The spectral even cycle problem, Combinatorial Theory 4 (1), (2024), #10, with Sebi Cioaba and Dheer Noal Desai.
A spectral Erdős-Sós theorem, SIAM Journal on Discrete Mathematics, Volume 37 Issue 3 (2023), with Sebi Cioaba and Dheer Noal Desai.
Sparsity of graphs with two distinct eigenvalues, Linear Algebra and its Applications, Volume 674, (2023), 377--395, with Wayne Barrett, Shaun Fallat, Vera Furst, Franklin Kenter, Shahla Nasserasr, Brendan Rooney, and Hein van der Holst
Extremal values for the spectral radius of the normalized distance Laplacian, Linear Algebra and its Applications 691, 37-49, with Jacob Johnston
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs, Linear Algebra and its Applications 679, 104-126, with Aida Abiad, Shaun Fallat, Mark Kempton, Rupert Levene, Polona Oblak, Helena Šmigoc, and Kevin Vander Meulen
Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues, Linear Algebra and its Applications 679, 127-164, with Wayne Barrett, Shaun Fallat, Vera Furst, Shahla Nasserasr, and Brendan Rooney
A general theorem in spectral extremal graph theory, with John Byrne and Dheer Noal Desai 🔥🔥🔥
Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues, with Wayne Barrett, Shaun Fallat, Vera Furst, Shahla Nasserasr, and Brendan Rooney
Expansion in Distance Matrices, with John Byrne, Jacob Johnston, and Carl Schildkraut
Miscellaneous
More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures. Electronic Journal of Combinatorics, 18.1, P26 (2011), with Sebastian Cioaba.
Variations on a theme of Graham and Pollak. Discrete Mathematics, Volume 313, Issue 5, 665--676 (2013). Co-authored with Sebastian Cioaba.
On Coupon Colorings of Graphs, Discrete Applied Mathematics 193 (2015), 94--101, with Bob Chen, Jeong Han Kim, and Jacques Verstraete.
On the chromatic number of the Erdős-Rényi orthogonal polarity graph. Electronic Journal of Combinatorics, P2.21, 1--19, (2015). With Sam Peng and Craig Timmons.
Independent sets in polarity graphs, SIAM Journal on Discrete Math, 30(4) (2016), 2115--2129, with Craig Timmons.
Increasing paths in edge-ordered graphs: the hypercube and random graphs. The Electronic Journal of Combinatorics, 23.2, P2.15, with Jessica De Silva, Theo Molla, Flo Pfender, and Troy Retter.
On a problem of Neumann , Discrete Math Special Issue on Algebraic and Extremal Graph Theory, 342 (10) (2019), 2843--2845.
Maximal planar subgraphs of fixed girth in random graphs, The Electronic Journal of Combinatorics, 25.2, (2018) P2.45, with Manuel Fernández and Nicholas Sieger.
Anti-Ramsey Multiplicities, The Australasian Journal of Combinatorics 73, (2019), 357--371, with Jess De Silva, Xiang Si, Yunus Tuncbilek, Ruifan Yang, and Michael Young.
On Edge-Colored Saturation Problems, Journal of Combinatorics 11(4) (2020), 639--655 with Mike Ferrara, Dan Johnston, Sarah Loeb, Flo Pfender, Alex Schulte, Heather Smith, Eric Sullivan, and Casey Tompkins.
Spectral radii of arithmetical structures on cycle graphs, Linear and Multilinear Algebra, published online April 2025, with Alexander Diaz-Lopez and Katie Haymaker.
Geometric structures in pseudo-random graphs, Canadian Journal of Mathematics, Volume 77, Issue 3, (June 2025), 1041 -- 1071, with Thang Pham, Steven Senger, and Vu Thi Huong Thu
VC-dimension and pseudo-random graphs, Discrete Applied Mathematics, Volume 365, (April 2025), 231--246, with Thang Pham, Steven Senger, and Nguyen Thu-Huyen
Theses
The Alon-Saks-Seymour and Rank-Coloring Conjectures M. Sc. Thesis, University of Delaware, 2011.
Connections between graph theory, additive combinatorics, and finite incidence geometry Ph.D. Thesis, UC San Diego, 2016.