# 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}
}
• Published in LATIN 31 March 2014
• Mathematics
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

### Homomorphisms of Signed Graphs

• Mathematics
J. 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

• Mathematics
ArXiv
• 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

• Mathematics
Electron. J. Comb.
• 2020

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

• Mathematics
Algorithmica
• 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

• Mathematics
CALDAM
• 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

• Mathematics
IPEC
• 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.

## References

SHOWING 1-10 OF 18 REFERENCES

### Homomorphisms of Signed Graphs

• Mathematics
J. 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 the complexity of H-coloring

• Mathematics
J. Comb. Theory, Ser. B
• 1990

### 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

### On homomorphisms to edge-coloured cycles

• Mathematics
Electron. Notes Discret. Math.
• 2000

### Complexity of Tree Homomorphisms

• Mathematics, Computer Science
Discret. Appl. Math.
• 1996

### Decomposition, approximation, and coloring of odd-minor-free graphs

• Mathematics
SODA '10
• 2010
These decomposition results provide new structural insights into odd-H-minor-free graphs, on the one hand generalizing the central structural result from Graph Minor Theory, and on the other hand providing an algorithmic decomposition into two bounded-treewidth graphs, generalizing a similar result for minors.

### Handbook of Constraint Programming

• Biology
Handbook of Constraint Programming
• 2006

### Signed Graphs

• Mathematics
Encyclopedia of Social Network Analysis and Mining
• 2014