On interval colourings of bi-regular bipartite graphs (Q2713634)

An edge coloring of a graph which uses integers as colors is called an interval coloring if for any vertex, the colors used on the edges incident with this vertex form an interval. It is an open question if every biregular bipartite graph allows an interval coloring. This conjecture is proved here for the case of \((2,d)\)-regular bipartite graphs (i.e., all vertices in one class of the bipartition have degree 2 and all vertices in the other class have degree \(d\)), for any odd \(d\). For even \(d\), the result follows from the Petersen theorem and was previously known.