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Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications.â€¦ (More)

- Lowell Abrams, Daniel C. Slilaty
- Journal of Graph Theory
- 2003

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G on the same edge set as Gâ€¦ (More)

- Daniel C. Slilaty
- Discrete Mathematics
- 2005

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Î£ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Î£ must be theâ€¦ (More)

- Daniel C. Slilaty, Hongxun Qin
- Discrete Mathematics
- 2007

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.

- Daniel C. Slilaty
- J. Comb. Theory, Ser. B
- 2007

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained byâ€¦ (More)

- Daniel C. Slilaty, Hongxun Qin
- Discrete Mathematics
- 2008

We discuss the relationship between the vertical connectivity of a biased graph Î© and the Tutte connectivity of the frame matroid of Î© (also known as the bias matroid of Î©).

- John Maharry, Daniel C. Slilaty
- Journal of Graph Theory
- 2012

There are several graphs H for which the precise structure of graphs that do not contain a minor isomorphic to H is known. In particular, such structure theorems are known for K5 [13], V8 [8] andâ€¦ (More)

- Daniel C. Slilaty, Hongxun Qin
- Discrete Mathematics
- 2008

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in theâ€¦ (More)

- Nancy Ann Neudauer, Daniel C. Slilaty
- J. Comb. Theory, Ser. B
- 2017

Given a group Î“ and a biased graph (G,B), we define a what is meant by a Î“-realization of (G,B) and a notion of equivalence of Î“-realizations. We prove that for a finite group Î“ and t â‰¥ 3, that thereâ€¦ (More)

- Lowell Abrams, Daniel C. Slilaty
- Eur. J. Comb.
- 2015

Given a graph G equipped with faithful and fixed-point-free Î“ -action (Î“ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closedâ€¦ (More)