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Graphs with Bounded Induced Distance

  • Serafino Cicerone
  • Gabriele Di Stefano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

In this work we introduce graphs with bounded induced distance of order k (BID(k) for short). In any graph belonging to BID(k), the length of every induced path between every pair of nodes is at most k times the distance between the same nodes. In communication networks modeled by these graphs any message can be always delivered through a path whose length is at most k times the best possible one, even if some nodes fail.

In this work we first provide a characterization of graphs in BID(k) by means of cycle-chord conditions. After that, we investigate classes with order k ≤ 2. In this context, we note that the class BID(1) is the well known class of distance-hereditary graphs, and show that 3/2 is a lower bound for the order k of graphs that are not distance-hereditary. Then we characterize graphs in BID(2/3) by means of their minimal forbidden induced subgraphs, and we also show that graphs in BID(2) have a more complex characterization. We prove that the recognition problem for the generic class BID(k) is Co-NP-complete. Finally, we show that the split composition can be used to generate graphs in BID(k).

Keywords

Short Path Steiner Tree Recognition Problem Node Failure Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Serafino Cicerone
    • 1
  • Gabriele Di Stefano
    • 1
  1. 1.Dipartimento di Ingegneria ElettricaUniversità degli Studi di L’AquilaMonteluco di Roio, L’AquilaItaly

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