A local approach to the Erdos-S\'os conjecture
Abstract
A famous conjecture of Erdos and S\'os states that every graph with average degree more than k - 1 contains all trees with k edges as subgraphs. We prove that the Erdos-S\'os conjecture holds approximately, if the size of the embedded tree is linear in the size of the graph, and the maximum degree of the tree is sublinear.
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