Diameter Determination on Restricted Graph Families

  • Derek G. Corneil
  • Feodor F. Dragan
  • Michel Habib
  • Christophe Paul
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)


Determining the diameter of a graph is a fundamental graph operation, yet no efficient (i.e. quadratic time) algorithm is known. In this paper, we examine the diameter problem on chordal and AT-free graphs and show that a very simple (linear time) 2-sweep Lex-BFS algorithm identifies a vertex of maximum eccentricity unless the given graph has a specified induced subgraph (it was previously known that a single Lex-BFS algorithm is guaranteed to end at a vertex that is within 1 of the diameter for chordal and AT-free graphs). As a consequence of the forbidden induced subgraph result on chordal graphs, our algorithm is guaranteed to work optimally for directed path graphs (it was previously known that a single LexBFS algorithm is guaranteed to work optimally for interval graphs).


Intersection Graph Switching Point Interval Graph Chordal Graph Arbitrary Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Derek G. Corneil
    • 1
  • Feodor F. Dragan
    • 2
  • Michel Habib
    • 3
  • Christophe Paul
    • 3
  1. 1.Dpt. of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Dpt. of Computer ScienceUniversity of RostockRostockGermany
  3. 3.LIRMMUMR CNRS-Université de Montpellier IIMontpellier Cedex 5France

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