L. Addario-berry, R. E. Aldred, K. Dalal, and B. A. Reed, Vertex colouring edge partitions, Journal of Combinatorial Theory, Series B, vol.94, issue.2, pp.237-244, 2005.
DOI : 10.1016/j.jctb.2005.01.001

L. Addario-berry, K. Dalal, and B. A. Reed, Degree constrained subgraphs, Discrete Applied Mathematics, vol.156, issue.7, pp.1168-1174, 2008.
DOI : 10.1016/j.dam.2007.05.059

A. Ahadi, A. Dehghan, M. Kazemi, and E. Mollaahmadi, Computation of lucky number of planar graphs is NP-hard, Information Processing Letters, vol.112, issue.4, pp.109-112, 2012.
DOI : 10.1016/j.ipl.2011.11.002

S. Akbari, M. Ghanbari, R. Manaviyat, and S. Zare, On the Lucky Choice Number of Graphs, Graphs and Combinatorics, vol.109, issue.2, pp.157-163, 2013.
DOI : 10.1007/s00373-011-1112-4

T. Bartnicki, J. Grytczuk, and S. Niwczyk, Weight choosability of graphs, Journal of Graph Theory, vol.85, issue.2, pp.242-256, 2009.
DOI : 10.1002/jgt.20354

T. Bartnicki, B. Bosek, S. Czerwi´nskiczerwi´nski, J. Grytczuk, G. Matecki et al., Additive Coloring of Planar Graphs, Graphs and Combinatorics, vol.117, issue.5, pp.1087-1098, 2014.
DOI : 10.1007/s00373-013-1331-y

F. Bonomo, G. Du´randu´ran, and J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Electronic Notes in Discrete Mathematics, vol.25, pp.41-47, 2006.
DOI : 10.1016/j.endm.2006.06.064

M. Borowiecki, J. Grytczuk, and M. Pil´sniakpil´sniak, Coloring chip configurations on graphs and digraphs, Information Processing Letters, vol.112, issue.1-2, pp.1-4, 2012.
DOI : 10.1016/j.ipl.2011.09.011

A. Brandt, J. Diemunsch, and S. Jahanbekam, Lucky choice number of planar graphs with given girth, 2015.

G. Chartrand, F. Okamoto, and P. Zhang, The Sigma Chromatic Number of a Graph, Graphs and Combinatorics, vol.91, issue.6, pp.755-773, 2010.
DOI : 10.1007/s00373-010-0952-7

S. Czerwi´nskiczerwi´nski, J. Grytczuk, ?. Wiktor, and . Zelazny, Lucky labelings of graphs, Inform

P. David and . Dailey, Uniqueness of colorability and colorability of planar 4-regular graphs are NPcomplete, Discrete Math, vol.30, issue.3, pp.289-293, 1980.

A. Dehghan, M. Sadeghi, and A. Ahadi, The complexity of the sigma chromatic number of cubic graphs

A. Dehghan, M. Sadeghi, and A. Ahadi, Algorithmic complexity of proper labeling problems, Theoretical Computer Science, vol.495, pp.25-36, 2013.
DOI : 10.1016/j.tcs.2013.05.027

D. Du, K. Ko, and J. Wang, Introduction to Computational Complexity, 2002.

M. R. Garey and D. S. Johnson, Computers and intractability: A guide to the theory of N P completeness, Bull. Amer. Math. Soc. (N.S.), vol.3, issue.2, pp.898-904, 1980.

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

M. Karo´nskikaro´nski, T. ?uczak, 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

M. Khatirinejad, R. Naserasr, M. Newman, B. Seamone, and B. Stevens, Digraphs are 2-weight choosable, ):Paper 21, 2011.

M. Khatirinejad, R. Naserasr, M. Newman, B. Seamone, and B. Stevens, Vertex-colouring edgeweightings with two edge weights, Discrete Math. Theor. Comput. Sci, vol.14, issue.1, pp.1-20, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00990567

M. Laso´nlaso´n, A generalization of combinatorial Nullstellensatz, Electron. J. Combin, vol.17, issue.6, 2010.

J. Marenco, M. Mydlarz, and D. Severín, Topological additive numbering of directed acyclic graphs, Information Processing Letters, vol.115, issue.2, pp.199-202, 2015.
DOI : 10.1016/j.ipl.2014.09.011

B. Seamone, Derived colourings of graphs, 2012.

D. B. West, Introduction to graph theory, 1996.