一般超图的张量谱性质

将一致超图的逆Perron值的概念推广到了一般超图上,并证明了超图G连通的充要条件为其逆Perron值大于0。同时给出了一般超图G的二分宽度、等周数、离心率基于逆Perron值的一些下界。最后,讨论了张量的可奇染色问题,得到非负对称弱不可约张量A可奇染色的充要条件为A的拉普拉斯张量和无符号拉普拉斯张量有相同的的谱。

Tensor spectral properties of general hypergraphs

In this paper, we extend the concepts of inverse Perron values to general hypergraphs. We show that a general hypergraph $\mathcal{G}$ is connected if and only if any inverse Perron values is large than 0. We give some bounds on the bipartition width, isoperimetric number, eccentricities and degrees of a hypergraph $\mathcal{G}$ in terms of inverse Perron values. Finally, we obtain that a weakly irreducible, nonnegative, symmetric tensor $A$ is odd-colorable if and only if its Laplacian tensor and the signless Laplacian tensor have the same spectral.