= Adjacency-preserving rooted-tree embedding
{title2=$T\leq_{\mathrm{adj}}S$}
An <adjacency-preserving rooted-tree embedding> is an injective vertex map preserving the root and every adjacency. Because each root-to-vertex path maps to a simple path of the same length, vertex depths are preserved. This is more restrictive than a <homeomorphic embedding of a rooted tree>, which may stretch edges into paths. The <branching-depth antichain of rooted trees> shows that the adjacency relation is not a <well-quasi-ordering>.
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