 
Summary: Fault tolerant graphs, perfect hash functions and disjoint paths
M. Ajtai
N. Alon
J. Bruck
R. Cypher
C.T. Ho
M. Naor
E. Szemer´edi
Abstract
Given a graph G on n nodes we say that a graph T on n + k nodes is a kfault tolerant
version of G, if we can embed G in any n node induced subgraph of T. Thus T can sustain
k faults and still emulate G without any performance degradation. We show that for a wide
range of values of n, k and d, for any graph on n nodes with maximum degree d there is a
kfault tolerant graph with maximum degree O(kd). We provide lower bounds as well: there
are graphs G with maximum degree d such that any kfault tolerant version of them has
maximum degree at least (d
k).
IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA
