 
Summary: On the Fault Tolerance of the Butterfly
Anna R. Karlin \Lambda Greg Nelson y Hisao Tamaki z
Abstract
We study the robustness of the butterfly network
against random static faults. Suppose that each
edge of the butterfly is present independently of
other edges with probability p. Our main result is
that there is a 01 law on the existence of a linear
sized component. More formally, there is a critical
probability p\Lambda such that for p above p\Lambda, the faulted
butterfly almost surely contains a linearsized com
ponent, whereas for p below p\Lambda, the faulted but
terfly almost surely does not contain a linearsized
component.
1 Introduction
Given a graph G, let G=p denote the random sub
graph obtained by considering each edge indepen
dently and including it in the subgraph with prob
ability p, excluding it with probability 1 \Gamma p. 1 We
call G=p a faulted version of G. A long list of theo
