On the Fault Tolerance of the Butter

We study the robustness of the butter y network against random static faults. Suppose that each edge of the butter y is present independently of other edges with probability p. Our main result is that there is a 0-1 law on the existence of a linearsized component. More formally, there is a critical probability p such that for p above p , the faulted butter y almost surely contains a linear-sized component, whereas for p below p , the faulted butter y almost surely does not contain a linear-sized component.