The complexity of the list homomorphism problem for signed graphs appears difficult to classify. Existing results focus on special classes of signed graphs, such as trees \cite{mfcs} and reflexive signed graphs \cite{ks}. Irreflexive signed graphs are in a certain sense the heart of the problem, as noted by a recent paper of Kim and Siggers. We focus on a special class of irreflexive signed graphs, namely those in which the unicoloured edges form a spanning path or cycle, which we call separable signed graphs. We classify the complexity of list homomorphisms to these separable signed graphs; we believe that these signed graphs will play an important role for the general resolution of the irreflexive case. We also relate our results to a conjecture of Kim and Siggers concerning the special case of weakly balanced irreflexive signed graphs; we have proved the conjecture in another paper, and the present results add structural information to that topic.

翻译：有符号图的列表同态问题的复杂性似乎难以分类。现有结果主要关注有符号图的特殊类别，例如树\cite{mfcs}和自反有符号图\cite{ks}。正如Kim和Siggers最近一篇论文所指出的，非自反有符号图在某种意义上构成了该问题的核心。我们聚焦于一类特殊的非自反有符号图，其中单色边构成一个生成路径或环，并将其称为可分离有符号图。我们分类了向这些可分离有符号图进行列表同态的复杂性；我们相信这些有符号图将对非自反情形的整体解决发挥重要作用。此外，我们将结果与Kim和Siggers关于弱平衡非自反有符号图特例的猜想联系起来；我们已在另一篇论文中证明了该猜想，而本文的结果为该课题补充了结构信息。