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Part of the book series: CRM Series ((CRMSNS,volume 16))

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Abstract

An edge colouring ϕ of a graph G is locally irregular if each colour class of ϕ induces a graph whose every adjacent vertices have distinct degrees. The least number \( X'_{irr} (G) \) of colours used by a locally irregular edge colouring of G (if any) is referred to as the irregular chromatic index of G.

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References

  1. M. Karoński, T. Luczak and A. Thomason, Edge weights and vertex colours, J. Combin. Theory, Ser, B 91(1) (2004), 151–157.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Addario-Berry, R. E. L. Aldred, K. Dalal and B. A. Reed, Vertex colouring edge partitions, J. Combin. Theory, Ser. B 94(2) (2005), 237–244.

    Article  MATH  MathSciNet  Google Scholar 

  3. O. Baudon, J. Bensmail, J. Przybyło and M. Woźniak, On decomposing regular graphs into locally irregular subgraphs, Preprint MD 065, http://www.ii.uj.edu.pl/preMD/index.php, 2013.

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Jaroslav Nešetřil Marco Pellegrini

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© 2013 Scuola Normale Superiore Pisa

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Bensmail, J. (2013). Complexity of determining the irregular chromatic index of a graph. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_104

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