论文标题
最小的非transvers-transvers hypergraphs和最小的非二角属超图
Minimal non-odd-transversal hypergraphs and minimal non-odd-bipartite hypergraphs
论文作者
论文摘要
在具有均匀性的所有均匀的超图中，从结构和光谱的角度来看，奇数转换或奇数两分的超图更接近两部分简单图。如果是非odd-transversal，则将其称为最小的非odd transversal，但删除任何边缘会导致奇数转换超图。在本文中，我们对最小非odd-transversal超图的同等表征，其发射机矩阵的等级超过$ \ mathbb {z} _2 $。如果最小的非transvers-transvers超图是均匀的，那么它甚至具有均匀性，因此是最小的非二级分支机构。我们表征了$ 2 $的均匀均匀的最小非第三型双方超图，并给出了一些$ d $的均匀均匀超图，这些均匀的超图是最小的非二级分支。最后，我们给出了最小的非第三部分超图的邻接张量的最小H-eigenvalue。
Among all uniform hypergraphs with even uniformity, the odd-transversal or odd-bipartite hypergraphs are more close to bipartite simple graphs from the viewpoint of both structure and spectrum. A hypergraph is called minimal non-odd-transversal if it is non-odd-transversal but deleting any edge results in an odd-transversal hypergraph. In this paper we give an equivalent characterization of the minimal non-odd-transversal hypergraphs by the degrees and the rank of its incidence matrix over $\mathbb{Z}_2$. If a minimal non-odd-transversal hypergraph is uniform, then it has even uniformity, and hence is minimal non-odd-bipartite. We characterize $2$-regular uniform minimal non-odd-bipartite hypergraphs, and give some examples of $d$-regular uniform hypergraphs which are minimal non-odd-bipartite. Finally we give upper bounds for the least H-eigenvalue of the adjacency tensor of minimal non-odd-bipartite hypergraphs.
