+\begin_inset Formula
+\[
+O\left(\log|V|\log\frac{1}{r-1}\right).
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Pause
+
+\end_layout
+
+\begin_layout Corollary
+In tournaments, paths can be constructed in logarithmic space.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+hyperlink{optimality}{
+\backslash
+beamergotobutton{More Details}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout AgainFrame
+\begin_inset Argument 1
+status collapsed
+
+\begin_layout Plain Layout
+7
+\end_layout
+
+\end_inset
+
+hierarchy
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+If a frame includes a program listing, the frame needs to be marked as
+\begin_inset Quotes eld
+\end_inset
+
+fragile
+\begin_inset Quotes erd
+\end_inset
+
+.
+ LyX has the FragileFrame layout for this.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout FragileFrame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Just a frame with a program code listing
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout FragileFrame
+This is some program code:
+\end_layout