7 citations · 11 across the 5 of their papers we have counts for
6 papers
Cobiased graphs: Single-element extensions and elementary quotients of graphic matroids
Daniel Slilaty, Thomas Zaslavsky
Zaslavsky (1991) introduced a graphical structure called a biased graph and used it to characterize all single-element coextensions and elementary lifts of graphic matroids. We int…
The family of bicircular matroids closed under duality
Vaidy Sivaraman, Daniel Slilaty
We characterize the 3-connected members of the intersection of the class of bicircular and cobicircular matroids. Aside from some exceptional matroids with rank and corank at most…
A Basic Structure for Grids in Surfaces
Lowell Abrams, Daniel Slilaty
A graph embedded in a surface is called an -grid when every facial boundary walk has length four, that is, the topological dual graph of in is 4-regular. Aside f…
Describing Quasi-Graphic Matroids
Nathan Bowler, Daryl Funk, Daniel Slilaty
This is a revised version of our original paper (arXiv:1808.00489v2) incorporating the corrections published in a corrigendum (arXiv:1808.00489v3). Our main theorem as originally s…
Matrix representations of frame and lifted-graphic matroids correspond to gain functions
Daryl Funk, Irene Pivotto, Daniel Slilaty
Let be a 3-connected matroid and let be a field. Let be a matrix over representing and let be a biased graph representing .…
Characterization of Line-Consistent Signed Graphs
Daniel C. Slilaty, Thomas Zaslavsky
The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Ac…