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dc.contributor.authorLladó Sánchez, Ana M.
dc.contributor.authorLópez Masip, Susana Clara
dc.contributor.authorMoragas Vilarnau, Jordi
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.identifier.citationLlado, A.; López, S.C.; Moragas, J. Every tree is a large subtree of a tree that decomposes Kn or Kn,n. "Discrete mathematics", 28 Febrer 2010, vol. 310, núm. 4, p. 838-842.
dc.description.abstractLet T be a tree with m edges. A well-known conjecture of Ringel states that T decomposes the complete graph $K_{2m+1}$. Graham and Häggkvist conjectured that T also decomposes the complete bipartite graph $K_{m,m}$. In this paper we show that there exists an integer n with n ≤[(3m - 1)/2] and a tree T₁ with n edges such that T₁ decomposes $K_{2n+1}$ and contains T. We also show that there exists an integer n' with n' ≥ 2m-1 and a tree T₂ with n' edges such that T₂ decomposes $K_{n',n'}$and contains T. In the latter case, we can improve the bound if there exists a prime p such that [3m/2] ≤ p < 2m - 1.
dc.format.extent5 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraph labelings
dc.subject.lcshGraph theory
dc.titleEvery tree is a large subtree of a tree that decomposes Kn or Kn,n
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
local.citation.authorLlado, A.; López, S.C.; Moragas, J.
local.citation.publicationNameDiscrete mathematics

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