最小弱饱和图与一般宿主图中的自举渗流
Minimum Weakly Saturated Graphs and Bootstrap Percolation in General Host Graphs
- Wesleyan College（卫斯理学院）
- Auburn University（奥本大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究最小弱饱和图类及其与H-自举渗流的关联，探讨一般宿主图下的弱饱和问题，明确了弱饱和数与最小弱饱和图的定义。
AI中文摘要：
图G是弱H-饱和的，若可通过逐次向G添加一条边得到完全图Kₙ，且每条新增边至少生成一个新的H副本。阶数为n的弱H-饱和图G所需的最少边数称为H的弱饱和数，记为wsat(n,H)。若对某一n值满足wsat(n,G)=|E(G)|-1，则称图G为最小弱饱和图。本文研究最小弱饱和图的各类及其与H-自举渗流过程的关联，还探讨了比完全图更一般情形下的弱饱和问题。
英文摘要：
A graph $G$ is weakly $H$-saturated if one can obtain $K_n$ by adding one edge to $G$ at a time, where each additional edge creates at least one new copy of $H$. The minimum number of edges needed for a weakly $H$-saturated graph $G$ of order $n$ is known as the weak saturation number of $H$, written $wsat(n,H)$. A graph $G$ is minimum weakly saturated if $wsat(n,G)=|E(G)|-1$ for some value of $n$. We explore classes of minimum weakly saturated graphs and their connection to the $H$-bootstrap percolation process, as well as weak saturation in a more general setting than the complete graph.
