An edge coloring of a graph G=(V,E) is a function c:E⇒ℕ that assigns a color c(e) to each edge e∈E such that c(e)≠c(e') whenever e and e' have a common endpoint. Denoting S
v
(G,c) the set of colors assigned to the edges incident to a vertex v∈V, and D
v
(G,c) the minimum number of integers which must be added to S
v
(G,c) to form an interval, the deficiency D(G,c) of an edge coloring c is defined as the sum Σ
v∈V
D
v
(G,c), and the span of c is the number of colors used in c. The problem of finding, for a given graph, an edge coloring with a minimum deficiency is NP-hard. We give new lower bounds on the minimum deficiency of an edge coloring and on the span of edge colorings with minimum deficiency. We also propose a tabu search algorithm to solve the minimum deficiency problem and report experiments on various graph instances, some of them having a known optimal deficiency.
