Signed graphs

Zaslavsky, Thomas

doi:10.1016/0166-218x(82)90033-6

Cited by 564 publications

(416 citation statements)

References 14 publications

Supporting

Mentioning

413

Contrasting

Unclassified

Order By: Relevance

“…A signed graph G can be switched to a signed graph H if there is a sequence of switchings applied to G that results in H. A signed graph is called balanced if it can be switched to the graph with all positive signs and unbalanced otherwise. It is well-known [6] that a signed graph is balanced if and only if all cycles of the graph contain an even number of negative edges.…”

Section: Introductionmentioning

confidence: 99%

Coloring signed graphs using DFS

Fleiner

Wiener

2015

Optim Lett

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Coloring signed graphs using DFS

Fleiner

Wiener

2015

Optim Lett

View full text Add to dashboard Cite

show abstract

“…It was first studied by Zaslavaky [11]. The matroid M (G, σ) of a bidirected graph is the column matroid of the incidence matrix B of the signed graph, where…”

Section: Lemma 21 [7] a Signed Graph Is Balanced If And Only If It Imentioning

confidence: 99%

Flows in 3-edge-connected bidirected graphs

Wei

Tang

2011

Front. Math. China

View full text Add to dashboard Cite

It was conjectured by A. Bouchet that every bidirected graph which admits a nowhere-zero k-flow admits a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. O. Zyka improved the result with 6 replaced by 30. R. Xu and C. Q. Zhang showed that the conjecture is true for 6-edge-connected graph, which is further improved by A. Raspaud and X. Zhu for 4-edge-connected graphs. The main result of this paper improves Zyka's theorem by showing the existence of a nowhere-zero 25-flow for all 3-edge-connected graphs.

show abstract

“…Closely related to the present paper are the work of Zaslavsky [12,13] and our recent paper [6]. Zaslavsky introduced some basic concepts of signed graphs such as circuit, bond, orientation, switching, incidence matrix, Laplacian, etc., and obtained an analog of the MatrixTree formula for graphs for unbalanced signed graphs; see [12]. Based on the work of Zaslavsky, the authors introduced coupling, characteristic vectors, circuit lattice, bond lattice, etc., and obtained the relations between them; see [6].…”

Section: Introductionmentioning

confidence: 98%

“…An important step is to discover a class of building blocks for dyadic matroids that play a similar role of graphs for regular matroids. Such building block candidates are naively expected to be the matroids derived by Zaslavsky [12] from signed graphs. The present paper supports this idea by showing that the signed graph matroids are indeed dyadic.…”

Section: Introductionmentioning

confidence: 99%

Torsion formulas for signed graphs

Chen

Wang

2010

Discrete Applied Mathematics

View full text Add to dashboard Cite

a b s t r a c tFollowing our recent exposition on the algebraic foundations of signed graphs, we introduce bond (circuit) basis matrices for the tension (flow) lattices of signed graphs, and compute the torsions of such matrices and Laplacians. We present closed formulas for the torsions of the incidence matrix, the Laplacian, bond basis matrices, and circuit basis matrices. These formulas show that the torsions of all such matrices are powers of 2, and so imply that the matroids of signed graphs are representable over any field of characteristic not 2. A notable feature of using torsion is that the Matrix-Tree formula for ordinary graphs and Zaslavsky's formula for unbalanced signed graphs are unified into one Matrix-Basis formula in terms of the torsion of its Laplacian matrix, rather than in terms of its determinant, which vanishes for an ordinary graph unless one row is deleted from the incidence matrix.

show abstract

Signed graphs

Cited by 564 publications

References 14 publications

Coloring signed graphs using DFS

Coloring signed graphs using DFS

Flows in 3-edge-connected bidirected graphs

Torsion formulas for signed graphs

Contact Info

Product

Resources

About