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A Variant of the Erd\H{o}s-S\'os Conjecture
A well-known conjecture of Erd\H{o}s and S\'os states that every graph with
average degree exceeding contains every tree with edges as a
subgraph. We propose a variant of this conjecture, which states that every
graph of maximum degree exceeding and minimum degree at least contains every tree with edges.
As evidence for our conjecture we show (i) for every there is a
such that the weakening of the conjecture obtained by replacing by
holds, and (ii) there is a such that the weakening of the conjecture
obtained by replacing by holds
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