Abstract
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.
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Cichacz, S., Görlich, A. Edge-disjoint Open Trails in Complete Bipartite Multigraphs. Graphs and Combinatorics 26, 207–214 (2010). https://doi.org/10.1007/s00373-010-0904-2
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DOI: https://doi.org/10.1007/s00373-010-0904-2