Research

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

Publications:

[13] Projective-planar graphs with no K_3,4-minor. J. Graph Theory, in press. (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:

Generalizing graphic hyperplane arrangements.

Some minor-closed classes of signed graphs. (Coauthored with Xiangqian Zhou)

Flexibility of Projective-Planar Embeddings (Coauthored with John Maharry, Neil Robertson, and Vaidy Sivaraman)

Research Grants Awarded:

[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.

Manuscripts in Preparation: (some are available by request)

[1] Cellular automorphisms and self duality

[2] A Dualization of Hoffman’s Circulation Theorem.

[3] Frame matroids within special classes of matroids.

[4] Matroid duality and topological duality for signed graphs.

[5] Generalized T-joins.

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.