Abstract

We consider the problem of realization of hypergraphs on a graph provided each hyperedge is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to Cycle Double Cover conjecture. We prove that checking the existence of realization is computationally hard. The hardness is proved in various settings: for realizations on all graphs, on simple graphs, and on graphs from several restricted classes.

中文翻译：

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使用同调路径的超图边缘表示

摘要

我们考虑图上超图的实现问题，假设每个超边由一个子图实现，其中恰好有两个顶点具有奇数度。这个问题与Cycle Double Cover猜想有关。我们证明，检查实现的存在在计算上是困难的。硬度在各种设置中得到证明：用于所有图、简单图以及来自几个受限类的图的实现。