K escapade

A K-escape refers to a concept in graph theory related to the minimum number of vertices that need to be removed from a graph to eliminate all copies of a specific subgraph, typically called a K, such as a complete graph of size K. Essentially, it measures how resistant a network is to fragmentation or the presence of specific connections. By identifying a small K-escape set, one can understand the network’s vulnerability or control points, which is useful in designing robust networks or analyzing their structural properties.