Advertisement

Graphs and Combinatorics

, Volume 10, Issue 2–4, pp 353–361 | Cite as

Neighbourhood-Perfect Line Graphs

  • Jenö Lehel†
Article

Abstract

We show that the line graph of any balanced hypergraph is neighbourhood-perfect. This result is a hypergraphic extension of a recent theorem in [GKLM] saying that the line graphs of bipartite graphs are neighbourhood-perfect. The note contains also a graphical extension of the same theorem: the characterization of all graphs with neighbourhood-perfect line graph. The proof relies on a characterization of neighbourhood-perfect graphs among line graphs in terms of forbidden induced subgraphs.

Keywords

Bipartite Graph Line Graph Maximal Clique Neighbourhood Graph Perfect Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berge, Graphs and Hypergraphs, North Holland, 1973Google Scholar
  2. 2.
    Gyárfás, ?., Kratsch, D., Lehel, J., Maffray, F.; Minimal non-neighbourhood-perfect graphs (submitted)Google Scholar
  3. 3.
    Lehel, J., Tuza, Zs.; Neighborhood-perfect graphs. Discrete Math. 61, 93–101 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Maffray, F.; Kernels in perfect line-graphs. J. Comb. Theory 55 (1992)Google Scholar
  5. 5.
    Neeralagi, P.S., Sampathkumar, E.; The neighbourhood number of a graph (manuscript, 1984)Google Scholar
  6. 6.
    Trotter, L.E.; Line perfect graphs. Math. Programming 12, 255–259 (1977)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jenö Lehel†
    • 1
  1. 1.Department of MathematicsCollege of Arts and Sciences, University of LouisvilleLouisvilleUSA

Personalised recommendations