Cleanup

Advanced/De Bruijn/parts/3 line.tex

@@ -1,7 +1,8 @@
 \section{Line Graphs}
 
 \problem{}
-Given a graph $G$, we can construct its \textit{line graph} (denoted $\mathcal{L}(G)$) by doing the following: \par
+Given a graph $G$, we can construct a graph called the \par
+\textit{line graph} of $G$ (\hspace{0.3ex}denoted $\mathcal{L}(G)$\hspace{0.3ex}) by doing the following: \par
 \begin{itemize}
 	\item Creating a node in $\mathcal{L}(G)$ for each edge in $G$
 	\item Drawing a directed edge between every pair of nodes $a, b$ in $\mathcal{L}(G)$ \par
@@ -93,7 +94,11 @@ Now, relabel the edge from $a$ to $b$ as $\texttt{x}\overline{\texttt{p}}\texttt
 Use these new labels to name nodes in $\mathcal{L}(G_n)$.
 
 \problem{}
-Construct $\mathcal{L}(G_2)$ and $\mathcal{L}(G_3)$. What do you notice?
+Construct $\mathcal{L}(G_2)$ and $\mathcal{L}(G_3)$. What do you notice? \par
+\hint{
+	What are $\mathcal{L}(G_2)$ and $\mathcal{L}(G_3)$? We've seen them before! \par
+	You may need to re-label a few edges.
+}
 
 \begin{solution}
 	After fixing edge labels, we find that