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单词 Branch
释义

branch


A subset B of a tree (T,<T) is a branch if B is a maximal linearly orderedPlanetmathPlanetmath subset of T. That is:

  • <T is a linear ordering of B

  • If tTB then B{t} is not linearly ordered by <T.

This is the same as the intuitive conception of a branch: it is a set of nodes starting at the root and going all the way to the tip (in infinite setsMathworldPlanetmath the conception is more complicated, since there may not be a tip, but the idea is the same). Since branches are maximal there is no way to add an element to a branch and have it remain a branch.

A cofinal branch is a branch which intersects every level of the tree.

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更新时间:2025/5/4 20:51:43