论文标题
匹配编号，哈密顿图和离散磁性拉普拉斯人
Matching number, Hamiltonian graphs and discrete magnetic Laplacians
论文作者
论文摘要
在本文中，我们将离散磁拉曲板（DML）的频谱与有限的简单图上的频谱相关联，具有图形的两个结构特性：存在完美匹配和基础图的汉密尔顿周期的存在。特别是，我们给出了一个光谱障碍物的家族，该家族通过磁性电位进行参数，以使图具有匹配（即具有完美的匹配）或Hamilton循环的存在。我们将分析基于[FCLP20A]中引入的光谱预订的特殊情况，并将磁性电位用作光谱控制参数。
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obstructions parametrised by the magnetic potential for the graph to be matchable (i.e., having a perfect matching) or for the existence of a Hamiltonian cycle. We base our analysis on a special case of the spectral preorder introduced in [FCLP20a] and we use the magnetic potential as a spectral control parameter.
