A comparison of integer and constraint programming models for the deficiency problem

• We describe integer and constraint programming models for the deficiency problem.
• We obtain bounds on the number of colors in an edge-coloring with minimum deficiency.
• We clearly show that symmetry breaking constraints decrease the computing time.

An edge-coloring of a graph G=(V,E)G=(V,E) is a function c that assigns an integer c(e  ) (called color) in {0,1,2,…}{0,1,2,…} to every edge e∈Ee∈E so that adjacent edges are assigned different colors. An edge-coloring is compact if the colors of the edges incident to every vertex form a set of consecutive integers. The deficiency problem is to determine the minimum number of pendant edges that must be added to a graph such that the resulting graph admits a compact edge-coloring. We propose and analyze three integer programming models and one constraint programming model for the deficiency problem.