H. Let and G. The, The vertices in A in H have even degrees, while the vertices in B have odd degrees. Thus, also H is locally irregular and ? irr

]. O. Baudon, J. Bensmail, J. Przybyy, and M. Wo´zniakwo´zniak, On decomposing regular graphs into locally irregular subgraphs, European Journal of Combinatorics, vol.49, pp.90-104, 2015.
DOI : 10.1016/j.ejc.2015.02.031

O. Baudon, J. Bensmail, and . Sopena, On the complexity of determining the irregular chromatic index of a graph, Journal of Discrete Algorithms, vol.30, pp.113-127, 2015.
DOI : 10.1016/j.jda.2014.12.008
URL : https://hal.archives-ouvertes.fr/hal-00921849

J. Bensmail and B. Stevens, Edge-partitioning graphs into regular and locally irregular components, Discrete Mathematics and Theoretical Computer Science, vol.17, issue.3, pp.43-58, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01058019

M. Kalkowski, M. Karo´nskikaro´nski, and F. Pfender, Vertex-coloring edge-weightings: Towards the 1-2-3-conjecture, Journal of Combinatorial Theory, Series B, vol.100, issue.3, pp.347-349, 2010.
DOI : 10.1016/j.jctb.2009.06.002
URL : https://doi.org/10.1016/j.jctb.2009.06.002

M. Karo´nskikaro´nski, T. Luczak, and A. Thomason, Edge weights and vertex colours, Journal of Combinatorial Theory, Series B, vol.91, issue.1, pp.151-157, 2004.
DOI : 10.1016/j.jctb.2003.12.001

L. M. Lovász, C. Thomassen, Y. Wu, and C. Zhang, Nowhere-zero 3-flows and modulo k -orientations, Journal of Combinatorial Theory, Series B, vol.103, issue.5, pp.587-598, 2013.
DOI : 10.1016/j.jctb.2013.06.003

J. Przybyy-lo, On decomposing graphs of large minimum degree into locally irregular subgraphs, Electronic Journal of Combinatorics, vol.23, issue.2, pp.2-31, 2016.

B. Seamone, The 1-2-3 Conjecture and related problems: a survey

C. Thomassen, The weak 3-flow conjecture and the weak circular flow conjecture, Journal of Combinatorial Theory, Series B, vol.102, issue.2, pp.521-529, 2012.
DOI : 10.1016/j.jctb.2011.09.003
URL : https://doi.org/10.1016/j.jctb.2011.09.003

C. Thomassen, Graph factors modulo k, Journal of Combinatorial Theory, Series B, vol.106, pp.174-177, 2014.
DOI : 10.1016/j.jctb.2014.01.002

C. Thomassen, Y. Wu, and C. Zhang, The 3-flow conjecture, factors modulo k , and the 1-2-3-conjecture, Journal of Combinatorial Theory, Series B, vol.121
DOI : 10.1016/j.jctb.2016.06.010
URL : https://doi.org/10.1016/j.jctb.2016.06.010