Almost every tree with m edges decomposes K2m,2m
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 i...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/28488 |
| Acesso em linha: | https://hdl.handle.net/2117/28488 https://dx.doi.org/10.1017/S0963548313000485 |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph theory Bipartition Complete bipartite graphs Complete graphs Equal sizes Random tree Grafs, Teoria de 05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | 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. |
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