Geodesic
Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 361-376

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We consider a list cost coloring of vertices and edges in the model of vertex, edge, total and pseudototal coloring of graphs. We use a dynamic programming approach to derive polynomial-time algorithms for solving the above problems for trees. Then we generalize this approach to arbitrary graphs with bounded cyclomatic numbers and to their multicolorings.
Keywords: cost coloring, dynamic programming, list coloring, NP-completeness, polynomial-time algorithm 
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     title = {Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs},
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Giaro, Krzysztof; Kubale, Marek. Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 361-376. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a10/