A general decomposition theory for the 1-2-3 Conjecture and locally irregular decompositions. Baudon, O., Bensmail, J., Davot, T., Hocquard, H., Przybylo, J., Senhaji, M., Sopena, É., & Wozniak, M. Discret. Math. Theor. Comput. Sci., 2019.
A general decomposition theory for the 1-2-3 Conjecture and locally irregular decompositions [link]Paper  bibtex   
@article{DBLP:journals/dmtcs/BaudonBDHPSSW19,
  author    = {Olivier Baudon and
               Julien Bensmail and
               Tom Davot and
               Herv{\'{e}} Hocquard and
               Jakub Przybylo and
               Mohammed Senhaji and
               {\'{E}}ric Sopena and
               Mariusz Wozniak},
  title     = {A general decomposition theory for the 1-2-3 Conjecture and locally
               irregular decompositions},
  journal   = {Discret. Math. Theor. Comput. Sci.},
  volume    = {21},
  number    = {1},
  year      = {2019},
  url       = {http://dmtcs.episciences.org/5334},
  timestamp = {Fri, 13 Mar 2020 00:00:00 +0100},
  biburl    = {https://dblp.org/rec/journals/dmtcs/BaudonBDHPSSW19.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

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