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

Autor
Balbuena, C.; Márquez, A.; Portillo, J.
Tipus d'activitat
Article en revista
Revista
Acta mathematica sinica, english series
Data de publicació
2011-01
Volum
27
Número
1
Pàgina inicial
135
Pàgina final
140
DOI
https://doi.org/10.1007/s10114-011-9617-6 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/12222 Obrir en finestra nova
URL
http://www.springerlink.com/content/52718460284v2241/ Obrir en finestra nova
Resum
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 ...
Citació
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.
Grup de recerca
COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions

Participants