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A sufficient degree condition for a graph to contain all trees of size k
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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