论文标题
概括禁止的诱导子图表的高节流数字
Generalizing forbidden induced subgraph characterizations of high throttling numbers
论文作者
论文摘要
零强迫是一个过程，该过程将信息的传播模拟整个图形的传播，因为使用颜色更改规则将白色顶点被迫将蓝色变为蓝色。 Butler和Young在2013年提出的节流的想法是优化最初的蓝色顶点数量与迫使所有顶点所花费的时间之间的权衡。图表的原始节流数可最大程度地减少这两个数量的总和，并且产品节流数量可最大程度地减少其产品。另外，加权节流的重量在最小化总和时会改变给这两个量的权重。自引入以来，节流已扩展到包括强迫零的许多变体。这激发了使用抽象色更改规则对零强迫和节流的研究。最近，已经显示出较高（总和）节流数字的图的特征是有限的禁忌诱导子图。在本文中，我们将该结果扩展到使用抽象的色彩更改规则的节流，产品节流和加权节流。为此，我们定义了一些重要的色彩更改规则的家庭，并探索其属性。
Zero forcing is a process that models the spread of information throughout a graph as white vertices are forced to turn blue using a color change rule. The idea of throttling, introduced in 2013 by Butler and Young, is to optimize the trade-off between the number of initial blue vertices and the time taken to force all vertices to become blue. The original throttling number of a graph minimizes the sum of these two quantities and the product throttling number minimizes their product. In addition, weighted throttling changes the weights given to these two quantities when minimizing their sum. Since its introduction, throttling has expanded to include many variants of zero forcing. This motivates the study of zero forcing and throttling using abstract color change rules. Recently, it has been shown that the graphs with high (sum) throttling numbers are characterized by a finite family of forbidden induced subgraphs. In this paper, we extend that result to throttling, product throttling, and weighted throttling using abstract color change rules. To this end, we define some important families of color change rules and explore their properties.
