## Abstract

For any \(k\in {\mathbb {N}}\), the *k*-subdivision of graph *G* is a simple graph \(G^{\frac{1}{k}}\), which is constructed by replacing each edge of *G* with a path of length *k*. In (Iradmusa in Discrete Math 310(10–11):1551–1556, 2010), the *m*th power of the *n*-subdivision of *G* has been introduced as a fractional power of *G*, denoted by \(G^{\frac{m}{n}}\). Wang and Liu (Discrete Math Algorithms Appl 10(3):1850041, 2018) showed that \(\chi (G^{\frac{3}{3}})\le 7\) for any subcubic graph *G*. In this note, a short proof is given for this theorem by use of incidence chromatic number.

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## References

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## Acknowledgement

The author is grateful to the referees for suggestions which improved the paper.

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### Cite this article

Iradmusa, M.N. A Short Proof of 7-Colorability of \(\frac{3}{3}\)-Power of Subcubic Graphs.
*Iran J Sci Technol Trans Sci* **44, **225–226 (2020). https://doi.org/10.1007/s40995-020-00819-1

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### Keywords

- Chromatic number
- Subdivision of a graph
- Power of a graph

### Mathematics Subject Classification

- 05C