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Decomposing almost complete graphs by random trees
dc.contributor.author | Lladó Sánchez, Ana M. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2015-05-13T11:30:43Z |
dc.date.created | 2014 |
dc.date.issued | 2014 |
dc.identifier.citation | Llado, A. Decomposing almost complete graphs by random trees. A: Jornadas de Matemática Discreta y Algorítmica. "IX Jornadas de Matemática Discreta y Algorítmica : Tarragona, 7-9 de Julio de 2014". Tarragona: 2014, p. 383-388. |
dc.identifier.uri | http://hdl.handle.net/2117/27908 |
dc.description.abstract | An old conjecture of Ringel states that every tree with m edges decom- poses the complete graph K 2 m +1 . A more general version of the Ringel’s conjecture says that every tree with m edges decomposes K rm +1 for each r = 2 provided that r and m + 1 are not both odd. The best lower bound for the order of a complete graph decomposed by a given tree with m edge is O ( m 3 ). We show that asymptotically almost surely a random tree with m edges and p = 2 m + 1 is a prime decomposes the complete graph minus one edge K 3 p - e . We also show that, for every prime of the form 2 km + 1 a random tree with m edges asymptotically almost surely decomposes the graph K 2 km +1 (3) obtained from the complete graph by replacing each vertex by the complement of a triangle. |
dc.format.extent | 6 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.other | Ringel Conjecture |
dc.subject.other | random trees |
dc.title | Decomposing almost complete graphs by random trees |
dc.type | Conference report |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | 05C Graph theory |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 15580375 |
dc.description.version | Postprint (published version) |
dc.date.lift | 10000-01-01 |
local.citation.author | Llado, A. |
local.citation.contributor | Jornadas de Matemática Discreta y Algorítmica |
local.citation.pubplace | Tarragona |
local.citation.publicationName | IX Jornadas de Matemática Discreta y Algorítmica : Tarragona, 7-9 de Julio de 2014 |
local.citation.startingPage | 383 |
local.citation.endingPage | 388 |