Research

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

Publications:

[11] The regular excluded minors for signed-graphic matroids. Combin. Probab. Comput., to appear. (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:

Integer functions on the cycle space and edges of a graph.

Generalizing graphic hyperplane arrangements.

Research Grants Awarded:

[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.

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 good friend and mentor Tom Zaslavsky.

Manuscripts in Preparation:

Matroid duality and topological duality for signed graphs.

3-Poised biased graphs.

Orientations of biased graphs and their matroids I, II, III.

Matroid lifts coming from linear transformations.

Flow/coloring duality in signed graphs.

Euclidean hyperplane arrangements and graph orientations.