Embedding nearly-spanning bounded degree trees

dc.creatorAlon, Noga
dc.creatorKrivelevich, Michael
dc.creatorSudakov, Benny
dc.date2007-06-27
dc.date.accessioned2026-07-07T08:12:49Z
dc.date.available2026-07-07T08:12:49Z
dc.descriptionWe derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1-ε)n vertices, in terms of the expansion properties of G. As a result we show that for fixed d\geq 2 and 0<ε<1, there exists a constant c=c(d,ε) such that a random graph G(n,c/n) contains almost surely a copy of every tree T on (1-ε)n vertices with maximum degree at most d. We also prove that if an (n,D,λ)-graph G (i.e., a D-regular graph on n vertices all of whose eigenvalues, except the first one, are at most λin their absolute values) has large enough spectral gap D/λas a function of d and ε, then G has a copy of every tree T as above.
dc.identifierhttps://arxiv.org/abs/0706.4100
dc.identifierhttp://arxiv.org/abs/0706.4100
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132588
dc.subjectCombinatorics
dc.titleEmbedding nearly-spanning bounded degree trees
dc.typetext

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