# Paths

### From G-designs

Relevant articles: _{[1]}.

# Paths

The path with vertices is denoted . Note that paths are trees.

## Spectrum Results

The spectrum problem for paths was completely settled by Tarsi in _{[1]}.

**Theorem 1**
_{[1]}

*Let . There exists a -design of order if and only if*

*or ; and**.*

## References

- ↑
^{1.0}^{1.1}^{1.2}Tarsi, M.*Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs*, J. Combin. Theory Ser. A,**34**, 60–70 (1983).