Abstract
In 1987, Alavi, Boals, Chartrand, Erdös, and Oellermann conjectured that all graphs have an ascending subgraph decomposition (ASD). Though different classes of graphs have been shown to have an ASD, the conjecture remains open. In this paper we investigate the similar problem for digraphs. In particular, we will show that any orientation of a compete balanced tripartite graph has an ASD.
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Alavi Y., Boals A.J., Chartrand G., Erdös P., Oellermann O.: The ascending subgraph decomposition problem. Congr. Numer. 58, 7–14 (1987)
Chartrand G., Lesniak L.: Graphs & Digraphs, 4th edn. Chapman & Hall/CRC, Boca Raton (2005)
Fu H.: A note on the ascending subgraph decomposition problem. Disc. Math. 84, 315–318 (1990)
Fu H., Hu W.: A note on ascending subgraph decompositions of regular graphs. Disc. Math. 253, 11–18 (2002)
Liu J.: The equipartite Oberwolfach problem with uniform tables. J. Comb. Theory Ser. A 101, 20–34 (2003)
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Wagner, B.C. Ascending Subgraph Decompositions in Oriented Complete Balanced Tripartite Graphs. Graphs and Combinatorics 29, 1549–1555 (2013). https://doi.org/10.1007/s00373-012-1208-5
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DOI: https://doi.org/10.1007/s00373-012-1208-5