论文标题
高级bootstrap渗透超图
High-order bootstrap percolation in hypergraphs
论文作者
论文摘要
由图形的引导程序渗透过程激发，我们将新的高阶概括定义为$ k $均匀的超图，其中我们会以某些整数$ 1 \ le j \ le j \ le K-1 $感染$ j $ j $ set的顶点。我们研究了最初感染的套件的最小尺寸，该套件最终会渗透并确定几乎所有$ k $和$ j $的情况下的确切大小。
Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to $k$-uniform hypergraphs, in which we infect $j$-sets of vertices for some integer $1\le j \le k-1$. We investigate the smallest possible size of an initially infected set which ultimately percolates and determine the exact size in almost all cases of $k$ and $j$.
