dc.contributor.author Balbuena Martínez, Maria Camino Teófila dc.contributor.author Márquez, Alberto dc.contributor.author Portillo, Jose Ramón dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III dc.date.accessioned 2011-04-04T09:52:41Z dc.date.available 2011-04-04T09:52:41Z dc.date.created 2011-01 dc.date.issued 2011-01 dc.identifier.citation Balbuena, C.; Márquez, A.; Portillo, J. A sufficient degree condition for a graph to contain all trees of size k. "Acta mathematica sinica, english series", Gener 2011, vol. 27, núm. 1, p. 135-140. dc.identifier.issn 1439-8516 dc.identifier.uri http://hdl.handle.net/2117/12222 dc.description.abstract The Erdős-Sós conjecture says that a graph G on n vertices and number of edges e(G) > n(k− 1)/2 contains all trees of size k. In this paper we prove a sufficient condition for a graph to contain every tree of size k formulated in terms of the minimum edge degree ζ(G) of a graph G defined as ζ(G) = min{d(u) + d(v) − 2: uv ∈ E(G)}. More precisely, we show that a connected graph G with maximum degree Δ(G) ≥ k and minimum edge degree ζ(G) ≥ 2k − 4 contains every tree of k edges if d G (x) + d G (y) ≥ 2k − 4 for all pairs x, y of nonadjacent neighbors of a vertex u of d G (u) ≥ k. dc.format.extent 6 p. dc.language.iso eng dc.publisher Springer Verlag dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria dc.subject.lcsh Extremal problems (Mathematics) dc.subject.lcsh Graph theory dc.subject.lcsh Combinatorial analysis dc.title A sufficient degree condition for a graph to contain all trees of size k dc.type Article dc.subject.lemac Problemes extrems (Matemàtica) dc.subject.lemac Grafs, Teoria de dc.subject.lemac Anàlisi combinatòria dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.1007/s10114-011-9617-6 dc.relation.publisherversion http://www.springerlink.com/content/52718460284v2241/ dc.rights.access Restricted access - publisher's policy local.identifier.drac 4598423 dc.description.version Postprint (published version) local.citation.author Balbuena, C.; Márquez, A.; Portillo, J. local.citation.publicationName Acta mathematica sinica, english series local.citation.volume 27 local.citation.number 1 local.citation.startingPage 135 local.citation.endingPage 140
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