# Papers

(categories are approximations!)

## Extremal graph theory

*On Coupon Colorings of Graphs*, Discrete Applied Mathematics 193 (2015), 94--101, with Bob Chen, Jeong Han Kim, and Jacques Verstraete.*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.*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.*The Zarankiewicz problem in 3-partite graphs*, Journal of Combinatorial Designs 27(6) (2019), 391--405, with Craig Timmons*Turán number of theta graphs*, to appear in Combinatorics, Probability and Computing 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*, to appear in Journal of Graph Theory with Juergen Kritschgau, Abhi Methuku, and Craig Timmons.*Large monochromatic components in 3-edge-colored Steiner triple systems*, to appear in Journal of Combinatorial Designs with Louis DeBiasio.

## 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 $\mathbb{Z}_n$, to appear in Integers 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)**,*with Robert Won

## 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 spectral radius of graphs with no intersecting triangles*, submitted with Sebi Cioaba, Lihua Feng, and Xiao-Dong Zhang.

## 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 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.*On Edge-Colored Saturation Problems**,*to appear in Journal of Combinatorics with Mike Ferrara, Dan Johnston, Sarah Loeb, Flo Pfender, Alex Schulte, Heather Smith, Eric Sullivan, and Casey Tompkins.

## 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.

# Collaborators

Ghodratollah Aalipour, Aida Abiad, Sinan Aksoy, Zhanar Berikkyzy, Anton Bernshteyn, Erin Bevilacqua, Boris Bukh, Bob Chen, Fan Chung, Sebi Cioaba, Jay Cummings, Jess De Silva, Louis DeBiasio, Sean English, Lihua Feng, Manuel Fernández, Mike Ferrara, Wei Gao, Daniel Gerbner, Sunny He, Kristin Heysse, Leslie Hogben, Alice Huang, Dan Johnston, Franklin Kenter, Jeong Han Kim, Sam King, Juergen Kritschgau, Jephian Lin, Sarah Loeb, Po-Shen Loh, Abhi Methuku, Theo Molla, Alp Muyesser, Vlado Nikiforov, Cory Palmer, Sam Peng, Flo Pfender, Thang Pham, Troy Retter, Alex Schulte, Xiang Si, Nicholas Sieger, Heather Smith, Suzannah Tebon, Craig Timmons, Josh Tobin, Casey Tompkins, Yunus Tuncbilek, Jacques Verstraëte, Le Anh Vinh, Adam Wagner, Rob Won, Ruifan Yang, Michael Young, Xioa-Dong Zhang, Rodrigo Zhou.

Honorable mentions (no papers [yet!]): Jane Breen, Steve Butler, Asaf Ferber, Paul Horn, Felix Lazebnik, Bernard Lidicky, Humberto Naves, Sankeerth Rao, John Urschel, Alex Vardy, Jason Williford.