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].
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Research supported by ONR Grant Number N00014-91-J-1098
Research supported by OTKA Grant Number 2570
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Jacobson, M.S., Kézdy, A.E. & Lehel, J. Recognizing Intersection Graphs of Linear Uniform Hypergraphs. Graphs and Combinatorics 13, 359–367 (1997). https://doi.org/10.1007/BF03353014
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DOI: https://doi.org/10.1007/BF03353014