__Research__

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

__Publications__

[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__

Coloring Permutation-Gain Graphs.

Hamilton cycles in bidirected complete graphs (Coauthored with Arthur Busch and Mohammed A. Mutar)

Matrix representations of frame and lifted-graphic matroids correspond to gain functions (Coauthored with Daryl Funk)

__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.