# 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}, 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…

## 14 Citations

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

- MathematicsDiscret. Math.
- 2017

### Homomorphisms of Signed Graphs

- MathematicsJ. Graph Theory
- 2015

This paper is the first general study of signed graph homomorphisms, and reformulating Hadwiger's conjecture in the language of homomorphism of signed graphs whose underlying graph is bipartite shows that while some stronger form of the conjecture holds for small chromatic number, such strengthening of the conjectures would not hold for large chromatic numbers.

### 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…

### 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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