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- Publications
- Influence

Projective-planar signed graphs and tangled signed graphs

- Daniel C. Slilaty
- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 1 September 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 by… Expand

On cographic matroids and signed-graphic matroids

- Daniel C. Slilaty
- Mathematics, Computer Science
- Discret. Math.
- 1 October 2005

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph @S iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that @S must be… Expand

Cellular automorphisms and self-duality

- L. Abrams, Daniel C. Slilaty
- Mathematics
- 20 May 2015

We catalog up to a type of reducibility all cellular automorphisms of the sphere, projective plane, torus, Klein bottle, and three-crosscaps (Dyck’s) surface. We also show how one can obtain all… Expand

Connectivity in frame matroids

- Daniel C. Slilaty, H. Qin
- Computer Science, Mathematics
- Discret. Math.
- 1 May 2008

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

Algebraic Characterizations of Graph Imbeddability in Surfaces and Pseudosurfaces

- L. Abrams, Daniel C. Slilaty
- Mathematics
- 1 August 2006

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.… Expand

An algebraic characterization of projective-planar graphs

- L. Abrams, Daniel C. Slilaty
- Computer Science
- J. 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 G… Expand

Decompositions of signed-graphic matroids

- Daniel C. Slilaty, H. Qin
- Mathematics, Computer Science
- Discret. Math.
- 1 August 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.

Bias matroids with unique graphical representations

- Daniel C. Slilaty
- Mathematics, Computer Science
- Discret. Math.
- 1 June 2006

Given a 3-connected biased graph @W with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of @W is uniquely represented by @W.

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic

- Daniel C. Slilaty
- Mathematics, Computer Science
- Comb. Probab. Comput.
- 1 September 2002

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic… Expand

The Regular Excluded Minors for Signed-Graphic Matroids

- H. Qin, Daniel C. Slilaty, X. Zhou
- Mathematics, Computer Science
- Comb. Probab. Comput.
- 1 November 2009

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),. . . , M*(G29), R15, R16. Here G1,. . . , G29 are the vertically 2-connected excluded… Expand