图和超图中的一致强制和免疫集
Uniform forcing and immune sets in graphs and hypergraphs
摘要：
迫零是一种在图上迭代着色的过程，它被广泛应用于网络传播现象的建模以及矩阵和图中最小秩问题的研究等不同领域。本文研究超图的迫零问题。（用超图表示网络，可以让我们解释网络的社区结构，以及不同节点子集之间更一般的交互。）我们考虑两个自然的推广超图的零强迫图（其中一个已经知道），对于每一个这些推广，我们看两个混乱，在强制过程中发挥了重要作用：混乱的最小强制集和最小免疫集之一。免疫集的制定方面的邻域（因此没有提到迭代迫零过程），突出不同的强制规则的不同行为。此外，我们得到的家庭的最小强制和最小免疫集的情况下，完全超图，我们提供了一个完整的表征强制和免疫均匀杂波，无论是在图和超图的情况下。
英文摘要：
Zero forcing is an iterative coloring process on a graph that has been widely used in such different areas as the modelling of propagation phenomena in networks and the study of minimum rank problems in matrices and graphs. This paper deals with zero forcing on hypergraphs. (Representing a network by a hypergraph allows us to account for its community structure and for more general interactions between different subsets of nodes.) We consider two natural generalizations to hypergraphs of zero forcing on graphs (one of them already known) and, for each one of these generalizations we look into two clutters that play a significant role in the forcing process: the clutter of minimal forcing sets and the one of minimal immune sets. A formulation of immune sets in terms of neighbourhoods (hence without making reference to the iterative zero forcing process) is presented, highlighting the different behaviour of the distinct forcing rules. Moreover, we obtain the families of minimal forcing and minimal immune sets in the case of complete hypergraphs and we provide a full characterization of forcing and immune uniform clutters, both in the graph and in the hypergraph case.
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