__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 K_{3,4}-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 Z_{n}-Symmetric
Graphs That Are Not Z_{n}-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 K_{3,4}-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 2*C*_{3}-minor and bicircular
matroids without a *U*_{3,6}-minor

Line Graphs of Directed Graphs I (with Vaidy Sivaraman)

Graphs without a *T*_{2,2,3}-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

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