Research

 

I am interested in topological and algebraic approaches to graph theory and matroid theory. 

  

Publications

[30] Matrix representations of frame and lifted-graphic matroids correspond to gain functions. J. Combin. Theory Ser. B., 155 (2022) 202–255. (With Daryl Funk and Irene Pivotto)

[29] Characterization of a Family of Rotationally Symmetric Spherical Quadrangulations. Ars Math. Contemp., 22 (2022) 35 pp. (Coauthored with Lowell Abrams)

[28] Hamilton cycles in bidirected complete graphs. Contrib. Discrete Math., 17 (2022), 137--149. (Coauthored with Arthur Busch and Mohammed A. Mutar)

[27] The family of bicircular matroids closed under duality. Graphs Combin., 38 (2022) Paper No. 24, 20 pp. (Coauthored with Vaidy Sivaraman)

[26] Coloring Permutation-Gain Graphs Contrib. Discrete Math., 16 (2021) 47–52.

[25] Describing Quasi-Graphic Matroids European J. Combin., 85 (2020) 103062, 26pp. (Coauthored with Nathan Bowler and Daryl Funk)

[24] The graphs that have antivoltages using groups of small order. Discrete Math., 342 (2019) 2951-2965. (Coauthored with Vaidy Sivaraman)

[23] Projective-planar graphs with no K3,4-minor. II. J. Graph Theory, 86 (2017) 92–103. (Coauthored with John Maharry)

[22] Flexibility of Projective-Planar Embeddings. J. Combin. Theory Ser. B, 122 (2017) 241–300. (Coauthored with John Maharry, Neil Robertson, and Vaidy Sivaraman)

[21] Bounding and stabilizing realizations of biased graphs with a fixed group. J. Combin. Theory Ser. B, 122 (2017) 149–166. (Coauthored with Nancy Neudauer)

[20] Bicircular matroids representable over GF(4) or GF(5). Discrete Math., 339 (2016) 2239–2248. (Coauthored with Deborah Chun, Tyler Moss, and Xiangqian Zhou)

[19] Clones in 3-Connected Frame Matroids. Discrete Math., 339 (2016) 1329–1334. (Coauthored with Jakayla Robbins and Xiangqian Zhou)

[18] Characterization of Line-Consistent Signed Graphs. Discuss. Math. Graph Theory, 35 (2015) 589–594 (Coauthored with Tom Zaslavsky)

[17] The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical. European J. Combin., 46 (2015) 95–114. (Coauthored with Lowell Abrams)

[16] Cellular automorphisms and self duality. Trans. Amer. Math. Soc., 367 (2015) 7695–7773. (Coauthored with Lowell Abrams)

[15] Unavoidable minors of large 4-connected bicircular matroids. Ann. Comb., 19 (2015) 95–105. (Coauthored with Deborah Chun, Tyler Moss, and Xiangqian Zhou)

[14] Some minor-closed classes of signed graphs. Discrete Math., 313 (2013) 313--325. (Coauthored with Xiangqian Zhou)

[13] Projective-planar graphs with no K3,4-minor. J. Graph Theory, 70 (2012) 121–239. (Coauthored with John Maharry)

[12] Integer functions on the cycle space and edges of a graph. Graphs Combin., 26 (2010) 293–299.

[11] The regular excluded minors for signed-graphic matroids.  Combin. Probab. Comput., 18 (2009) 953–978. (Coauthored with Hongxun Qin and Xiangqian Zhou)

[10] Connectivity in frame matroids. Discrete Math., 308 (2008) 1994--2001. (Coauthored with Hongxun Qin)

[9] The signed-graphic representations of wheels and whirls. Discrete Math., 308 (2008) 1816--1825. (Coauthored with Hongxun Qin)

[8] Decompositions of signed-graphic matroids. Discrete Math., 307 (2007) 2187--2199. (Coauthored with Hongxun Qin.)

[7] Projective-planar signed graphs and tangled signed graphs. J. Combin. Theory Ser. B, 97 (2007) 693--717.

[6] Algebraic characterizations of graph imbeddability in surfaces and pseudosurfaces. J. Knot Theory Ramifications, 15 (2006) 681--693. (Coauthored with Lowell Abrams.)

[5] Bias matroids with unique graphical representations. Discrete Math., 306 (2006) 1253--1256.

[4] On cographic matroids and signed-graphic matroids. Discrete Math., 301 (2005) 207--217.

[3] An algebraic characterization of projective-planar graphs. J. Graph Theory, 42 (2003) 320--331. (Coauthored with Lowell Abrams.)

[2] Matroid duality from topological duality in surfaces of nonnegative Euler characteristic. Combin. Probab. Comput., 11 (2002) 515--528.

[1] Bounds on squares of two-sets. Ars Combin., 42 (1996) 181--191. (Coauthored with Jeffrey Vanderkam.)

 

Papers Submitted for Publication

Orientations of golden-mean matroids (Coauthored with Jakayla Robbins) Supplemental material

Signed Ramsey Numbers (Coauthored with Mohammed Mutar and Vaidy Sivaraman)

Odd Solutions to Systems of Inequalities Coming From Regular Chain Groups

Graphs without a 2C3-minor and bicircular matroids without a U3,6-minor

Line Graphs of Directed Graphs I (with Vaidy Sivaraman)

Graphs without a T2,2,3-minor

 

Research Grants Awarded

[6] Algorithms on Generalized Networks. A Seedling Grant from the Defense Advanced Research Projects Agency (DARPA) Awarded October 2016, $99,620

[5] Topological graph theory and matroid theory. Simons Foundation Collaboration Grants for Mathematicians. Awarded August 2012, $35,000

[4] Fundamental classes of matroids and matroid representability. A Research Initiation Grant from Wright State University. Awarded in May 2009. $10,000 Co-PI with Xiangqian Zhou.

[3] Decompositions of biased graphs and flow-coloring duality of imbedded graphs. A Young Investigators Grant from the National Security Agency. Awarded in October 2006. $30,000.

[2] Signed graphs and dyadic matroids. A Young Investigators Grant from the National Security Agency. Awarded in October 2004. $26,000.

[1] Matroid theory and network flows. A Research Challenges New Investigator Grant from Wright State University. Awarded in May 2002. $5,000.

 

Masters Theses Supervised

[2] Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers, Mohammed A. Mutar, Fall 2017.

[1] Symmetric colorings of the hypercube and hyperoctahedron. Bo Phillips, Spring 2016.

 

My Doctoral Dissertation

Orientations of biased graphs and their matroids. (2000) State University of New York at Binghamton.

During my time in graduate school I was advised by my friend and mentor Tom Zaslavsky.