A note on the bounded fragmentation property and its applications in network reliability

Authors:
Mohammad Taghi Hajiaghayi;Mahdi Hajiaghayi
Affiliations:
Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge;Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
Venue:
European Journal of Combinatorics
Year:
2003

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Abstract

In this paper, we introduce a new property for graphs called bounded fragmentation, by which we mean after removing any set of at most k vertices the number of connected components is bounded only by a function of k. We demonstrate how bounded fragmentation can be used to measure the reliability of a network and introduce several classes of bounded fragmentation graphs. Finally, we pose some open problems related to this concept.