# Homomorphisms of Signed Graphs

@article{Naserasr2015HomomorphismsOS, title={Homomorphisms of Signed Graphs}, author={Reza Naserasr and Edita Rollov{\'a} and {\'E}ric Sopena}, journal={Journal of Graph Theory}, year={2015}, volume={79} }

A signed graph [G,Σ] is a graph G together with an assignment of signs + and − to all the edges of G where Σ is the set of negative edges. Furthermore [G,Σ1] and [G,Σ2] are considered to be equivalent if the symmetric difference of Σ1 and Σ2 is an edge cut of G. Naturally arising from matroid theory, several notions of graph theory, such as the theory of minors and the theory of nowhere‐zero flows, have been already extended to signed graphs. In an unpublished manuscript, B. Guenin introduced…

## 86 Citations

### The homomorphism order of signed graphs

- Mathematics
- 2020

A signed graph (G, σ) is a graph G together with a mapping σ which assigns to each edge of G a sign, either positive or negative. The sign of a closed walk in (G, σ) is the product of the signs of…

### The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction

- MathematicsLATIN
- 2014

The more general concept of signed constraint satisfaction problems is introduced and it is shown that a dichotomy for such problems is equivalent to the statement of the Feder-Vardi Dichotomy Conjecture.

### Extended Double Covers and Homomorphism Bounds of Signed Graphs

- Mathematics
- 2021

A signed graph (G,σ) is a graph G together with an assignment σ : E(G) → {+,−}. The notion of homomorphisms of signed graphs is a relatively new development which allows to strengthen the connection…

### The complexity of signed graph and edge-coloured graph homomorphisms

- MathematicsDiscret. Math.
- 2017

### On homomorphisms of planar signed graphs and absolute cliques

- Mathematics
- 2019

A simple signed graph (G,Σ) is a simple graph with a + or a − sign assigned to each of its edges where Σ denotes the set of negative edges. A closed-walk is unbalanced if it has an odd number of…

### Mapping sparse signed graphs to $(K_{2k}, M)$

- Mathematics
- 2021

A homomorphism of a signed graph ( G, σ ) to ( H, π ) is a mapping of vertices and edges of G to (respectively) vertices and edges of H such that adjacencies, incidences and the product of signs of…

### Classification of edge-critical underlying absolute planar cliques for signed graphs

- Mathematics
- 2020

A simple signed graph (G,Σ) is a simple graph G having two different types of edges, positive edges and negative edges, where Σ denotes the set of negative edges of G. A closed walk of a signed graph…

## References

SHOWING 1-10 OF 51 REFERENCES

### The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction

- MathematicsLATIN
- 2014

The more general concept of signed constraint satisfaction problems is introduced and it is shown that a dichotomy for such problems is equivalent to the statement of the Feder-Vardi Dichotomy Conjecture.

### Homomorphisms of Edge-Colored Graphs and Coxeter Groups

- Mathematics
- 1998

AbstractLet
$$G_1 = (V_1 ,E_1 ){\text{ and }}G_2 = (V_2 ,E_2 )$$
be two edge-colored graphs (without multiple edges or loops). A homomorphism is a mappingϕ :
$$V_1 \mapsto V_2 $$
for which, for…

### Characterizations of signed graphs

- MathematicsJ. Graph Theory
- 1981

Two characterizations are given here of the possible classes of balanced circles of a signed graph: an elementary one of the balanced portion of an arbitrary subclass of circles, and a strongerOne of the entire balanced circle class.

### Circular flows of nearly Eulerian graphs and vertex‐splitting

- MathematicsJ. Graph Theory
- 2002

The odd edge connectivity of a graph G, denoted by o(G), is the size of a smallest odd edge cut of the graph such that any graph G embedded in S with the odd-edge connectivity at least fS( ) admits a nowhere-zero circular (2þ )-flow.

### Homomorphisms of planar signed graphs to signed projective cubes

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2013

It is shown that for a given g, this conjecture is equivalent to the corresponding case of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable.

### Homomorphisms of signed planar graphs

- MathematicsArXiv
- 2014

Using the properties of some target graphs for signed homomorphism, upper bounds are obtained on the signed chromatic numbers of graphs with bounded acyclic chromatic number and of signed planar graphs with given girth.