Asteroidal triple-free graphs

  • Derek. G. Corneil
  • Stephan Olariu
  • Lorna Stewart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 790)


Many families of perfect graphs such as interval graphs, permutation graphs, trapezoid graphs and cocomparability graphs demonstrate a type of linear ordering of their vertex sets. These graphs are all subfamilies of a class of graphs called the asteroidal triple-free graphs. (An independent triple {x, y, z} is called an asteroidal triple (AT, for short) if between any pair in the triple there exists a path that avoids the neighbourhood of the third vertex.) In this paper we argue that the property of being AT-free is what is enforcing the linear ordering of the vertex sets. To justify this claim, we present various structural properties and characterizations of AT-free graphs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Derek. G. Corneil
    • 1
  • Stephan Olariu
    • 2
  • Lorna Stewart
    • 3
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Department of Computer ScienceOld Dominion UniversityNorfolkUSA
  3. 3.Department of Computer ScienceUniversity of AlbertaEdmontonCanada

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