As part of a more general categorization of the class of line graphs of linear 3-uniform hypergraphs with minimum
vertex degree at least 19, Metelsky and Tyshkevich (1997) established that a
graph with minimum vertex degree at least
5 is a line graph iff it does
not contain any of a subset of 6 of the Beineke graphs
as an induced subgraph.

These graphs, illustrated above, are known in this work as Metelsky graphs and are implemented in the Wolfram Language
as `GraphData`[`"Metelsky"`].

## See also

Beineke Graphs,

Forbidden Induced Subgraph,

Line Graph,

Šoltes
Graphs
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## References

Metelsky, Yu. and Tyshkevich, R. "On Line Graphs of
Linear 3-Uniform Hypergraphs." *J. Graph Th.* **25**, 243-251, 1997.
## Cite this as:

Weisstein, Eric W. "Metelsky Graphs."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MetelskyGraphs.html

## Subject classifications