论文标题
泄漏强迫的概括
Generalizations of Leaky Forcing
论文作者
论文摘要
最近引入了顶点泄漏强迫，作为零强迫的新变化，以说明顶点泄漏如何破坏图中的零强迫过程。边缘泄漏是一个边缘，在零强迫过程中不允许跨越。 $ \ ell $ - 边缘裂变的图形的强迫数是最小的零强迫集的大小，尽管$ \ ell $ ed $ edge泄漏，但仍可以迫使图形蓝色。本文包含了边缘泄漏对零强迫过程的影响而不是顶点泄漏的分析。此外，还引入了指定的$ \ ell $ -leaky强迫。主要的结果是$ \ ell $ -leaky强迫，$ \ ell $ -Edge-Leaky迫使和指定的$ \ ell $ -leaky-leaky强迫是等效的。此外，所有这些不同类型的泄漏都可以混合，以便使用顶点泄漏，边缘泄漏和指定的泄漏。这个混合的$ \ ell $ -leaky强迫号也与（vertex）$ \ ell $ -leaky强迫号码相同。
Vertex leaky forcing was recently introduced as a new variation of zero forcing in order to show how vertex leaks can disrupt the zero forcing process in a graph. An edge leak is an edge that is not allowed to be forced across during the zero forcing process. The $\ell$-edge-leaky forcing number of a graph is the size of a smallest zero forcing set that can force the graph blue despite $\ell$ edge leaks. This paper contains an analysis of the effect of edge leaks on the zero forcing process instead of vertex leaks. Furthermore, specified $\ell$-leaky forcing is introduced. The main result is that $\ell$-leaky forcing, $\ell$-edge-leaky forcing, and specified $\ell$-leaky forcing are equivalent. Furthermore, all of these different kinds of leaks can be mixed so that vertex leaks, edge leaks, and specified leaks are used. This mixed $\ell$-leaky forcing number is also the same as the (vertex) $\ell$-leaky forcing number.
