Fix line lengths

1 files changed, 9 insertions, 7 deletions

diff --git a/mgr.tex b/mgr.tex
index 00e45a9..217e99d 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -120,8 +120,9 @@ dependence on tree size during question answering.
 
 More explicitly, we will show how to solve Problem
 \ref{mso-query-answering-problem}, with a preprocessing algorithm working in
-time $O_{\varphi}(n)$ (where $n$ is the size of the input tree), and then answer questions
-in time $O_{\varphi}(m \log m)$ (where $m$ is the size of the question):
+time $O_{\varphi}(n)$ (where $n$ is the size of the input tree), and then answer
+questions in time $O_{\varphi}(m \log m)$ (where $m$ is the size of the
+question):
 
 \queryproblem[%
     an MSO formula $\varphi(\vec{X})$ over trees with $k$ free
@@ -848,8 +849,9 @@ $W \subseteq V(T)$ is \definedterm{partition ready} if
 \begin{enumerate}
     \item it is LCA closed;
     \item it contains the root of the tree;
-    \item\label{both-subtrees-property} for every $v \in W$, either it has descendants in $W$ in at most one
-        of its subtrees, or both of its children are elements of $W$.
+    \item\label{both-subtrees-property} for every $v \in W$, either it has
+        descendants in $W$ in at most one of its subtrees, or both of its
+        children are elements of $W$.
 \end{enumerate}
 
 We will define the \definedterm{LCA partition with respect to $W$} for a
@@ -862,9 +864,9 @@ Each part will be of one of three types:
 \begin{description}
     \item[subtree] A \definedterm{subtree of $v$} is $v$ along with all its descendants;
         it is rooted in $v$.
-    \item[subtree with hole] A \definedterm{subtree of $v$ with hole $w$} is the subtree of $v$
-        minus the subtree of $w$ (for $w$ a descendant of $v$); it is rooted in
-        $v$.
+    \item[subtree with hole] A \definedterm{subtree of $v$ with hole $w$} is the
+        subtree of $v$ minus the subtree of $w$ (for $w$ a descendant of $v$);
+        it is rooted in $v$.
     \item[singleton] A singleton vertex $v$, which is the root of such a part.
 \end{description}