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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.date.accessioned2011-04-04T09:52:41Z
dc.date.available2011-04-04T09:52:41Z
dc.date.created2011-01
dc.date.issued2011-01
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.identifier.issn1439-8516
dc.identifier.urihttp://hdl.handle.net/2117/12222
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.language.isoeng
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.typeArticle
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.identifier.doi10.1007/s10114-011-9617-6
dc.relation.publisherversionhttp://www.springerlink.com/content/52718460284v2241/
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac4598423
dc.description.versionPostprint (published version)
local.citation.authorBalbuena, C.; Márquez, A.; Portillo, J.
local.citation.publicationNameActa mathematica sinica, english series
local.citation.volume27
local.citation.number1
local.citation.startingPage135
local.citation.endingPage140


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