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Neighbourhood-Perfect Line Graphs

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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.

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References

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, University of Louisville, KY40292, Louisville, USA

    Jenö Lehel†

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  1. Jenö Lehel†
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Research partly supported by OTKA grant No 2570

† On leave from the Computer and Automation Research Institute, Hungarian Academy of Sciences

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Lehel†, J. Neighbourhood-Perfect Line Graphs. Graphs and Combinatorics 10, 353–361 (1994). https://doi.org/10.1007/BF02986685

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  • DOI: https://doi.org/10.1007/BF02986685

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