Research
I am interested in topological and algebraic approaches to graph theory and matroid theory.
Publications
[34] Odd Solutions to Systems of Inequalities Coming from Regular Chain Groups, Discrete Math. Lett. (2023), accepted for publication.
[33] Graphs without a 2C3-minor and bicircular matroids without a U3,6-minor, Trans. Comb., (2023), accepted for publication.
[32] Orientations of golden-mean matroids, J. Combin. Theory Ser. B, 162 (2023) 71–117. (Coauthored with Jakayla Robbins) Supplemental material
[31] Representations of signed graphs, J. Algebraic Combin., (2023) accepted for publication. (with Yu Qing Chen, Anthony Evans, Xiaoyu Liu, and Xiangqian Zhou)
[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
Signed Ramsey Numbers (Coauthored with Mohammed Mutar and Vaidy Sivaraman)
Line Graphs of Directed Graphs I (with Vaidy Sivaraman)
On Colorings and Orientations of Signed Graphs
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
During my time in graduate school I was advised by my friend and mentor Tom Zaslavsky.