-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 506
\begin_document
\begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
\textclass beamer
\begin_preamble
\beamertemplateshadingbackground{red!5}{structure!5}
\language_package default
\inputencoding auto
\fontencoding global
-\font_roman times
-\font_sans default
-\font_typewriter default
-\font_math auto
+\font_roman "times" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
+\font_sf_scale 100 100
+\font_tt_scale 100 100
\graphics default
\default_output_format default
\output_sync 0
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
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+\begin_inset Separator parbreak
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+
+
\end_layout
\begin_deeper
\begin_layout Columns
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
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+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
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-\begin_layout Separator
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+\end_inset
+
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+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\begin_layout Columns
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+\end_inset
+
\end_layout
\color inherit
is a
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+
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-\begin_layout Separator
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+
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+
+
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+
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+\end_inset
+
+
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\begin_deeper
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+\end_inset
+
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+\begin_inset Separator parbreak
+\end_inset
+
+
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+\end_inset
+
+
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+\end_inset
+
+
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\begin_deeper
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+\begin_inset Separator parbreak
+\end_inset
+
+
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+\end_inset
+
+
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\begin_deeper
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+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\begin_layout Corollary
For directed graphs, we can solve
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
-complete.
\end_layout
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
such that
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
such that
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\color inherit
gets as input
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_deeper
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
.
- LyX has the FragileFrame layout for this.
+ \SpecialChar LyX
+ has the FragileFrame layout for this.
\end_layout
\end_inset
\begin_layout FragileFrame
This is some program code:
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
.
\end_layout
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_layout
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\begin_layout Corollary
For undirected graphs, we can solve
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_inset
+\begin_inset Separator parbreak
+\end_inset
+
+
\end_layout
\begin_deeper
\end_layout
\begin_layout Proof
+\begin_inset Separator parbreak
+\end_inset
+
\end_layout