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Polynomial Time Complexity of Edge Colouring Graphs with Bounded Colour Classes

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Abstract

We show that the following fundamental edge-colouring problem can be solved in polynomial time for any given constant B: given a simple graph G, find an edge-colouring of G where each colour is assigned to at most B edges and which, subject to this condition, has the fewest number of colour classes.

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Notes

  1. \(\lceil \frac{m}{a} \rceil \leq b\) and \(\lceil \frac{m}{b} \rceil \leq a\) are both equivalent to m≤ab.

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Acknowledgements

A special thanks goes to the anonymous referee for his/her inspiring and valuable help, and for the many and detailed suggestions.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Romeo Rizzi

  2. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou Higher Education Town, Jiangsu, 215123, China

    David Cariolaro

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  1. Romeo Rizzi
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  2. David Cariolaro
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Correspondence to David Cariolaro.

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Rizzi, R., Cariolaro, D. Polynomial Time Complexity of Edge Colouring Graphs with Bounded Colour Classes. Algorithmica 69, 494–500 (2014). https://doi.org/10.1007/s00453-013-9746-7

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  • DOI: https://doi.org/10.1007/s00453-013-9746-7

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