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

@inproceedings{Foucaud2014TheCO, title={The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction}, author={Florent Foucaud and Reza Naserasr}, booktitle={Latin American Symposium on Theoretical Informatics}, year={2014} }

A signed graph (G, Σ) is an undirected graph G together with an assignment of signs (positive or negative) to all its edges, where Σ denotes the set of negative edges. Two signatures are said to be equivalent if one can be obtained from the other by a sequence of resignings (i.e. switching the sign of all edges incident to a given vertex). Extending the notion of usual graph homomorphisms, homomorphisms of signed graphs were introduced, and have lead to some extensions and strengthenings in the…

## 16 Citations

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

- MathematicsDiscret. Math.
- 2017

### On cliques of signed and switchable signed graphs

- MathematicsArXiv
- 2014

It is shown that it is NP-hard to decide if edges of a given undirected graph can be assigned positive and negative signatures such that it becomes an sclique or an [s]-clique, and it is proved that, asymptotically, almost all signed graphs are scliques or [s]cliques.

### Homomorphisms of Sparse Signed Graphs

- MathematicsElectron. J. Comb.
- 2020

The restriction of homomorphisms of signed graphs on sparse families is studied and it is proved that for any given signed graph, there exists a positive value of $\epsilon$ such that, if $G$ is a connected graph of maximum average degree less than $2+\ep silon, it admits a homomorphism to $UC_{2g}$.

### List homomorphism problems for signed graphs

- MathematicsMFCS
- 2020

The list homomorphisms of signed graphs are considered from a computational perspective and the complexity of the problem when $H$ is a (reflexive or ir Reflexive) tree is classified.

### Graph Modification for Edge-Coloured and Signed Graph Homomorphism Problems: Parameterized and Classical Complexity

- MathematicsAlgorithmica
- 2022

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from an edge-coloured graph G to an…

### Graph Modification for Edge-Coloured and Signed Graph Homomorphism Problems: Parameterized and Classical Complexity

- MathematicsAlgorithmica
- 2022

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from an edge-coloured graph G to an…

### Relative Clique Number of Planar Signed Graphs

- MathematicsCALDAM
- 2016

The exact values of signed relative clique number of the families of outerplanar graphs and triangle-free planar graphs are determined.

### Parameterized complexity of edge-coloured and signed graph homomorphism problems

- MathematicsIPEC
- 2019

The complexity of graph modification problems for homomorphism-based properties of edge-coloured graphs is studied, and a P/NP-complete complexity dichotomy is given for all three studied problems.

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