A graph with minimum vertex degree at least 5 is a line graph iff it does
not contain any of the above six graphs, known in this work as Metelsky graphs, as
an induced subgraph (Metelsky and Tyshkevich
1997). These six graphs are implemented in the Wolfram
Language as `GraphData`[`"Metelsky"`].

# Metelsky Graphs

## See also

Beineke Graphs, Forbidden Induced Subgraph, Line Graph## Explore with Wolfram|Alpha

## 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