Edge-disjoint Open Trails in Complete Bipartite Multigraphs

Let ^r K _a,b be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph ^r K _a,b to be arbitrarily decomposable into open trails. We extend the results obtained by Balister for complete graphs (Balister in Probab Comput 10:463–499, 2001). Moreover we show that a multigraph ^r K _a,b with even r and a ≥ 3 or b ≥ 3 is arbitrarily decomposable into open and closed trails.