, Volume 20, Issue 4, pp 571-577

A Solution to a Problem of Jacobson, Kézdy and Lehel

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Abstract.

We solve a problem proposed by Jacobson, Kézdy, and Lehel [4] concerning the existence of forbidden induced subgraph characterizations of line graphs of linear k-uniform hypergraphs with sufficiently large minimal edge-degree. Actually, we prove that for each k≥3 there is a finite set Z(k) of graphs such that each graph G with minimum edge-degree at least 2k 2−3k+1 is the line graph of a linear k-uniform hypergraph if and only if G is a Z(k)-free graph.

Acknowledgments. We thank the anonymous referees, whose suggestions helped to improve the presentation of the paper.
Winter 2002/2003 DIMACS Award is gratefully acknowledged
2000 Mathematics Subject Classification: 05C65 (05C75, 05C85)