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Graphs and Combinatorics

, Volume 13, Issue 4, pp 359–367 | Cite as

Recognizing Intersection Graphs of Linear Uniform Hypergraphs

  • Michael S. Jacobson
  • André E. Kézdy
  • Jenő Lehel
Article

Abstract

A hypergraph is linear if any two distinct hyperedges have at most one common vertex. The existence of a polynomial algorithm is shown for deciding whether a graph of minimum degree δ ≥ 19 is the intersection graph of a linear 3-uniform hypergraph. This result improves a corollary of the finite forbidden subgraph characterization proved for δ ≥ 69 by Naik et al. in [8]. Essentially the same methods yield a polynomial recognition algorithm for the intersection graph of a linear r-uniform hypergraph, r ≥ 3, provided the minimum edge-degree of the graphs is at least 2r 2 − 3r + 1. This improves on the cubic bound that follows from the corresponding finite characterization result in [8].

Keywords

Minimum Degree Maximal Clique Intersection Graph Polynomial Algorithm Common Vertex 
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 1997

Authors and Affiliations

  • Michael S. Jacobson
    • 1
  • André E. Kézdy
    • 1
  • Jenő Lehel
    • 1
  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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