= Half-sparse median-order embedding
{title2=$|f(T)\cap I|<|I|/2+1$}
= Half-sparse embedding
{synonym}
A <graph embedding> into an ordered <tournament> is half-sparse when the displayed inequality holds for every proper final interval $I$. Reserving two extra tournament vertices allows extension at any outward-oriented leaf: the <median order of a tournament> supplies at least half of the later vertices as outneighbours of the parent's image, while half-sparsity leaves at least one of them unused. Adding one image while extending every old final interval by two preserves the inequality.
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