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A Short Proof of 7-Colorability of \(\frac{3}{3}\)-Power of Subcubic Graphs

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 mth 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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Acknowledgement

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

Author information

Correspondence to Moharram N. Iradmusa.

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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