Multilayer graphs consist of several graphs, called layers, where the vertex set of all layers is the same but each layer has an individual edge set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multilayer graphs, including fundamental problems such as maximum-cardinality matching, finding certain clique relaxations, or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of computational tractability.

中文翻译：

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评估多层子图检测的计算复杂度

多层图由多个图组成，称为层，其中所有层的顶点集相同，但每一层都有单独的边集。它们的动机是现实世界的问题，其中实体（顶点）通过多种类型的关系（不同层中的边）关联。我们绘制了多层图上子图检测问题类的计算（难）易处理性边界，包括诸如最大基数匹配、寻找某些团松弛或路径问题等基本问题。大多是遇到硬度结果，有时甚至是两三层，我们也可以发现一些计算易处理性的孤岛。