论文标题
Bunkbed的猜想，用于完整的两部分图和相关类图的类别
Bunkbed conjecture for complete bipartite graphs and related classes of graphs
论文作者
论文摘要
令$ g =（v，e）$为一个简单的有限图。 The corresponding bunkbed graph $G^\pm$ consists of two copies $G^+ = (V^+,E^+),G^- = (V^-,E^-)$ of $G$ and additional edges connecting any two vertices $v_+ \in V_+,v_- \in V_-$ that are the copies of a vertex $v \in V$.铺位的猜想指出，对于$ g^\ pm $上的独立债券渗透，对于所有$ v，w \ in v $，与$ v _-，w _- $相比，要连接$ v _- $更有可能连接。虽然这似乎非常合理，但到目前为止，鲜为人知的很少。最近，已证明了该猜想的完整图。在这里，我们给出了完整的两部分图的证明，完整图减去完整子图的边缘和对称完整的$ K $ - 分段图。
Let $G = (V,E)$ be a simple finite graph. The corresponding bunkbed graph $G^\pm$ consists of two copies $G^+ = (V^+,E^+),G^- = (V^-,E^-)$ of $G$ and additional edges connecting any two vertices $v_+ \in V_+,v_- \in V_-$ that are the copies of a vertex $v \in V$. The bunkbed conjecture states that for independent bond percolation on $G^\pm$, for all $v,w \in V$, it is more likely for $v_-,w_-$ to be connected than for $v_-,w_+$ to be connected. While this seems very plausible, so far surprisingly little is known rigorously. Recently the conjecture has been proved for complete graphs. Here we give a proof for complete bipartite graphs, complete graphs minus the edges of a complete subgraph, and symmetric complete $k$-partite graphs.
