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| -rw-r--r-- | mgr.tex | 8 |
1 files changed, 6 insertions, 2 deletions
@@ -1052,8 +1052,8 @@ Consider the subtree of $v$ with hole $w$. It can be divided into the following components: \begin{itemize} - \item A path from $w$ up to $v$, notate it as $u_0 = w, u_1, \ldots, u_p = - v$. + \item A path from the parent of $w$ up to $v$, notate it as $u_1, u_2, + \ldots, u_p = v$. \item For each $i$ from 1 to $p$, the subtree of $u_i$'s child that doesn't lie on the path from $w$ to $v$. Let $u_i'$ be the child of $u_i$ that doesn't lie on the $w$ to $v$ path. @@ -1070,6 +1070,10 @@ components: }\label{subtree-with-hole-figure} \end{figure} +$w$ is not a part of the subtree with hole, but we will need to consider it +during the following computation, so for ease of notation we will let $u_0 = +w$, extending the path of $u_i$'s. + Figure \ref{subtree-with-hole-figure} depicts a subtree with hole labeled according to this nomenclature. |