Large bounded degree trees in expanding graphs

J́ozsef Balogh, B́ela Csaba, Martin Pei, Wojciech Samotij

Research output: Contribution to journalArticlepeer-review


A remarkable result of Friedman and Pippenger [4] gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. Haxell [5] showed that under slightly stronger assumptions on the expansion rate, their technique allows one to find arbitrarily large trees with bounded maximum degree. Using a slightly weaker version of Haxell's result we prove that a certain family of expanding graphs, which includes very sparse random graphs and regular graphs with large enough spectral gap, contains all almost spanning bounded degree trees. This improves two recent tree-embedding results of Alon, Krivelevich and Sudakov [1].

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 2010
Externally publishedYes


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