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dc.contributor.authorBalbuena Martínez, Maria Camino Teófila
dc.contributor.authorMárquez, Alberto
dc.contributor.authorPortillo, Jose Ramón
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.identifier.citationBalbuena, 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.description.abstractThe 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.extent6 p.
dc.publisherSpringer Verlag
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshExtremal problems (Mathematics)
dc.subject.lcshGraph theory
dc.subject.lcshCombinatorial analysis
dc.titleA sufficient degree condition for a graph to contain all trees of size k
dc.subject.lemacProblemes extrems (Matemàtica)
dc.subject.lemacGrafs, Teoria de
dc.subject.lemacAnàlisi combinatòria
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.authorBalbuena, C.; Márquez, A.; Portillo, J.
local.citation.publicationNameActa mathematica sinica, english series

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