Abstract: An edge-coloring of a graph G with colors 1,2,…,t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form a continuous interval of integer. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. The set of all interval colorable graphs is denoted by N. The deficiency def(G)of a graph G is the minimum number of pendant edges whose attachment to G makes it interval colorable. Obviously, G∈N if and only if def(G)=0. A generalized θ-chain, denoted by θ_m1,m2,…,m_k, is a simple graph obtained by substituting each edge v_i-1v_i of the path P=［v0,v1,…,v_k］(k≥1)for m_i≥2 pairwise internally disjoint(v_i-1,v_i)-paths, where i=1,2,…,k. In this paper, the conclusions of deficiency of generalized θ-graph are generalized, and the deficiency of the generalized θ-chain θ_m1,m2,…,m_k is determined.

Key words: interval edge-coloring, deficiency, generalized θ-graph, generalized θ-chain