论文标题
具有多项式表示的超图：介绍$ r $ splits
Hypergraphs with Polynomial Representation: Introducing $r$-splits
论文作者
论文摘要
受图形和排名宽度的分裂分解的启发，我们介绍了$ r $ -splits的概念。我们专注于订单$ n $的$ r $ splits家族，我们证明它形成了具有多个属性的超图。我们证明，尽管具有指数级的Hyperedges数量，但只能使用其HypereDges的$ \ Mathcal O（N^{r+1}）$表示此类超图。我们还证明，使用集合正交性的概括，存在至少需要$ω（n^r）$ hyperedges来表示的超图。
Inspired by the split decomposition of graphs and rank-width, we introduce the notion of $r$-splits. We focus on the family of $r$-splits of a graph of order $n$, and we prove that it forms a hypergraph with several properties. We prove that such hypergraphs can be represented using only $\mathcal O(n^{r+1})$ of its hyperedges, despite its potentially exponential number of hyperedges. We also prove that there exist hypergraphs that need at least $Ω(n^r)$ hyperedges to be represented, using a generalization of set orthogonality.
