论文标题
定向超图：均衡性
Oriented Hypergraphs: Balanceability
论文作者
论文摘要
面向的超图是一种定向的入射率结构，可扩展签名图，平衡超图和平衡矩阵的概念。我们通过其当地签名的循环子结构介绍了将签名的图形框架矩阵的电路分类概括到任何方向的超图形矩阵中的高图结构和技术。为此，将CAMION的算法应用于定向的超图，以提供重新定位集和挫败感的概括，这些算法仅在可平衡的方向超图上明确定义。不可兑现的电路的简单部分表征将应用程序扩展到可表示的矩形，表明Fano和非Fano Matroids之间的差异是平衡之一。
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.
