Improved Bounds for Minimum Fault-Tolerant Gossip Graphs

  • Toru Hasunuma
  • Hiroshi Nagamochi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)


A k-fault-tolerant gossip graph is a (multiple) graph whose edges are linearly ordered such that for any ordered pair of vertices u and v, there are k + 1 edge-disjoint ascending paths from u to v. Let τ(n,k) denote the minimum number of edges in a k-fault-tolerant gossip graph with n vertices. In this paper, we present upper and lower bounds on τ(n,k) which improve the previously known bounds. In particular, from our upper bounds, it follows that \(\tau(n,k) \leq \frac{nk}{2} + O(n\log{n})\). Previously, it has been shown that this upper bound holds only for the case that n is a power of two.


Telephone Call Exchange Path Small Factor Center Vertex Circulant Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Toru Hasunuma
    • 1
  • Hiroshi Nagamochi
    • 2
  1. 1.Institute of Socio-Arts and SciencesThe University of TokushimaTokushimaJapan
  2. 2.Department of Applied Mathematics and PhysicsKyoto UniversityKyotoJapan

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