Forbidden induced subgraphs for line graphs. (English) Zbl 0805.05072

Summary: We prove that a connected graph with at least nine vertices is a line graph if and only if it does not contain any of the seven given graphs as an induced subgraph. We also show that the number seven cannot be reduced even if the number of vertices is increased.


05C75 Structural characterization of families of graphs
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[1] Beineke, L. W., Derived graphs and digraphs, (Beiträge zur Graphentheorie (1968), Teubner: Teubner Leipzig), 17-33 · Zbl 0179.29204
[2] Cvetković, D.; Doob, M.; Simić, S., Generalized line graphs, J. Graph Theory, 5, 385-399 (1981) · Zbl 0475.05061
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