Almost every tree with m edges decomposes K2m,2m

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/28488

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Drmota, Michael
dc.contributor.author	Lladó Sánchez, Ana M.
dc.date	2014-01
dc.identifier.citation	Drmota, 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.
dc.identifier.citation	0963-5483
dc.identifier.citation	10.1017/S0963548313000485
dc.identifier.uri	http://hdl.handle.net/2117/28488
dc.language.iso	eng
dc.relation	http://journals.cambridge.org/action/displayAbstract?aid=9098773
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject	Graph theory
dc.subject	Bipartition
dc.subject	Complete bipartite graphs
dc.subject	Complete graphs
dc.subject	Equal sizes
dc.subject	Random tree
dc.subject	Grafs, Teoria de
dc.subject	05C Graph theory
dc.title	Almost every tree with m edges decomposes K2m,2m
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	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.
dc.description.abstract	Peer Reviewed

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