Abstract
A conjecture of Graham and Häggkvist says that every tree with m edges decomposes the complete bipartite graph K m,m . By establishing some properties of random trees with the use of singularity analysis of generating functions, we prove that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K 2m,2m .
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Drmota, M., Lladó, A. (2013). On a conjecture of Graham and Häggkvist for random trees. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_70
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DOI: https://doi.org/10.1007/978-88-7642-475-5_70
Publisher Name: Edizioni della Normale, Pisa
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