Almost every tree with m edges decomposes K2m,2m
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We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size. © Cambridge University Press 2013.
CitationDrmota, M.; Llado, A. Almost every tree with m edges decomposes K2m,2m. "Combinatorics probability and computing", Gener 2014, vol. 23, núm. 1, p. 50-65.