On the deficiency of bipartite graphs Original Research Article

Given a graph G, an edge-coloring of G with colors 1,2,3,… is consecutive if the colors of edges incident to each vertex form an interval of integers. This paper is devoted to bipartite graphs which do not have such a coloring of edges. We investigate their consecutive coloring deficiency, or shortly the deficiency d(G) of G, i.e. the minimum number of pendant edges whose attachment to G makes it consecutively colorable. In particular, we show that there are bipartite graphs whose deficiency approaches the number of vertices.