# 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}
}
• Published 15 September 2013
• Mathematics
• Journal of Graph Theory
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 In an unpublished manuscript, B. Guenin introduced…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

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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.

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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.

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• Mathematics
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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.