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Signed graphs have been introduced to enrich graph structures expressingrelationships between persons or general social entities, introducing edgesigns to reflect the nature of the relationship, e.g., friendship or enmity.Independently, offensive alliances have been defined and studied forundirected, unsigned graphs. We join both lines of research and defineoffensive alliances in signed graphs, hence considering the nature ofrelationships. Apart from some combinatorial results, mainly on k-balanced andk-anti-balanced signed graphs (where the latter is a newly introduced family ofsigned graphs), we focus on the algorithmic complexity of finding smallestoffensive alliances, looking at a number of parameterizations. While theparameter solution size leads to an FPT result for unsigned graphs, we obtainW[2]-completeness for the signed setting. We introduce new parameters forsigned graphs, e.g., distance to weakly balanced signed graphs, that could beof independent interest. We show that these parameters yield FPT results. Here,we make use of the recently introduced parameter neighborhood diversity forsigned graphs.

Offensive Alliances in Signed Graphs