French UserGuide.lyx: another update from Jean-Pierre

[lyx.git] / lib / examples / beamerlyxexample1.lyx

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 341212c46758c968adc1c6ff5f3d5c327e52dc8e..f595947dedf296f3aa5be2cead5cf40a4ac6c3f2 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,7 +1,9 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 459
+#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}
@@ -155,16 +157,16 @@
 \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
@@ -177,6 +179,7 @@
 \use_geometry false
 \use_package amsmath 2
 \use_package amssymb 2
+\use_package cancel 0
 \use_package esint 0
 \use_package mathdots 1
 \use_package mathtools 0
@@ -185,7 +188,7 @@
 \use_package stmaryrd 0
 \use_package undertilde 0
 \cite_engine basic
-\cite_engine_type numerical
+\cite_engine_type default
 \biblio_style plain
 \use_bibtopic false
 \use_indices false
@@ -248,10 +251,24 @@ ICSI
 January 30th, 2004
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Outline
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset CommandInset toc
 LatexCommand tableofcontents
@@ -272,13 +289,10 @@ status collapsed
 
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \begin_inset ERT
-status collapsed
+status open
 
 \begin_layout Plain Layout
 
@@ -341,11 +355,28 @@ Introduction
 What are Tournaments?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments Consist of Jousts Between Knights
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Columns
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -535,6 +566,10 @@ What is a Tournament?
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -579,11 +614,36 @@ In every joust one knight wins.
 
 \end_deeper
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments are Complete Directed Graphs
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Columns
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -811,6 +871,10 @@ tournament
  
 \color inherit
 is a
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -828,20 +892,42 @@ any two different vertices.
 
 \end_deeper
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-[<+>]
++
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments Arise Naturally in Different Situations
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout ExampleBlock
 \begin_inset Argument 2
 status collapsed
@@ -853,6 +939,10 @@ Applications in Ordering Theory
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -866,7 +956,10 @@ The comparison relation may be cyclic, however.
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -881,6 +974,10 @@ Applications in Sociology
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -894,7 +991,10 @@ Reviewers decide for any two candidates whom they prefer.
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -909,6 +1009,10 @@ Applications in Structural Complexity Theory
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -932,15 +1036,30 @@ It chooses from any two words the one more likely to be in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection
 What Does ``Finding Paths'' Mean?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 ``Finding Paths'' is Ambiguous
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status open
@@ -1074,6 +1193,10 @@ the Approximation Problem
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1210,6 +1333,10 @@ status open
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1224,6 +1351,10 @@ t,onlytextwidth
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1297,6 +1428,10 @@ Example Input
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1686,6 +1821,10 @@ Example Output
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1912,6 +2051,10 @@ status open
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -1926,6 +2069,10 @@ Variants of Path Finding Problems
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2096,6 +2243,7 @@ Problem: Construct a path from
 approximately their distance.
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout Section
@@ -2125,7 +2273,11 @@ pgfdeclareimage[height=2cm,mask=computer-mask,interpolate=true]{computer}{beamer
 
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Classes L and NL are Defined via
 \begin_inset Newline newline
 \end_inset
@@ -2133,6 +2285,16 @@ The Classes L and NL are Defined via
 Logspace Turing Machines
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -2296,10 +2458,32 @@ end{pgfpicture}
 
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Logspace Turing Machines Are Quite Powerful
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status collapsed
@@ -2311,6 +2495,10 @@ Deterministic logspace machines can compute
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2342,6 +2530,10 @@ Non-deterministic logspace machines can compute
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2358,20 +2550,52 @@ satisfiability with two literals per clause.
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 1
 status collapsed
 
 \begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 3
+status collapsed
 
-<1>[label=hierarchy]
+\begin_layout Plain Layout
+label=hierarchy
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Complexity Class Hierarchy
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -2755,7 +2979,19 @@ end{pgfpicture}
 
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Circuit Complexity Classes AC
 \begin_inset Formula $^{0}$
 \end_inset
@@ -2775,6 +3011,16 @@ The Circuit Complexity Classes AC
 Limit the Circuit Depth
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -2811,6 +3057,10 @@ t
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2833,6 +3083,10 @@ Circuit Class
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2849,6 +3103,9 @@ unbounded fan-in
 
 \end_deeper
 \begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -2891,6 +3148,10 @@ Circuit Class
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2907,6 +3168,9 @@ bounded fan-in
 
 \end_deeper
 \begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -2956,6 +3220,10 @@ Circuit Class
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -2972,6 +3240,9 @@ bounded fan-in
 
 \end_deeper
 \begin_layout Examples
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -2983,6 +3254,7 @@ bounded fan-in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout AgainFrame
@@ -3002,7 +3274,11 @@ hierarchy
 Standard Complexity Results on Finding Paths
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 All Variants of Finding Paths in Directed Graphs
 \begin_inset Newline newline
 \end_inset
@@ -3010,15 +3286,25 @@ All Variants of Finding Paths in Directed Graphs
 Are Equally Difficult
 \end_layout
 
-\begin_layout Fact
-\begin_inset Formula $\Lang{reach}$
 \end_inset
 
- and 
-\begin_inset Formula $\Lang{distance}$
+
+\begin_inset Separator parbreak
 \end_inset
 
- are 
+
+\end_layout
+
+\begin_deeper
+\begin_layout Fact
+\begin_inset Formula $\Lang{reach}$
+\end_inset
+
+ and 
+\begin_inset Formula $\Lang{distance}$
+\end_inset
+
+ are 
 \begin_inset Formula $\Class{NL}$
 \end_inset
 
@@ -3032,6 +3318,10 @@ Are Equally Difficult
 
 \begin_layout Corollary
 For directed graphs, we can solve
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3067,6 +3357,7 @@ the approximation problem in logspace iff
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -3081,7 +3372,11 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Finding Paths in Forests and Directed Paths is Easy,
 \begin_inset Newline newline
 \end_inset
@@ -3089,6 +3384,16 @@ Finding Paths in Forests and Directed Paths is Easy,
 But Not Trivial
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{forest}}$
 \end_inset
@@ -3104,7 +3409,10 @@ But Not Trivial
 -complete.
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -3123,6 +3431,7 @@ But Not Trivial
 -complete.
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
 status collapsed
@@ -3144,10 +3453,24 @@ Finding Paths in Tournaments
 Complexity of: Does a Path Exist?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Definition of the Tournament Reachability Problem
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
 Let
 \color none
@@ -3166,6 +3489,10 @@ contain all triples
 \end_inset
 
  such that
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3197,10 +3524,32 @@ there exists a path from
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Tournament Reachability Problem is Very Easy
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 \begin_inset Formula $\Lang{reach}_{\operatorname{tourn}}\in\Class{AC}^{0}$
 \end_inset
@@ -3223,6 +3572,10 @@ Implications
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3253,6 +3606,7 @@ easier
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -3271,7 +3625,11 @@ hierarchy
 Complexity of: Construct a Shortest Path
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Finding a Shortest Path Is as Difficult as
 \begin_inset Newline newline
 \end_inset
@@ -3279,6 +3637,16 @@ Finding a Shortest Path Is as Difficult as
 the Distance Problem
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
 Let
 \color none
@@ -3297,6 +3665,10 @@ contain all tuples
 \end_inset
 
  such that 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3332,10 +3704,32 @@ the distance of
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Tournament Distance Problem is Hard
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3396,7 +3790,19 @@ in logarithmic space, iff
 .
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Proof That 
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3404,6 +3810,16 @@ Proof That
  is NL-complete
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -3431,6 +3847,10 @@ t,onlytextwidth
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3475,6 +3895,10 @@ Reduce
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -3542,7 +3966,10 @@ Query:
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -3567,6 +3994,10 @@ status open
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -4692,6 +5123,7 @@ end{pgfpicture}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -4710,10 +5142,24 @@ hierarchy
 Complexity of: Approximating the Shortest Path
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Approximators Compute Paths that Are Nearly As Short As a Shortest Path
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
 An
 \color none
@@ -4728,6 +5174,10 @@ approximation scheme for
  
 \color inherit
 gets as input
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -4772,7 +5222,19 @@ a path from
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 There Exists a Logspace Approximation Scheme for
 \begin_inset Newline newline
 \end_inset
@@ -4780,6 +5242,16 @@ There Exists a Logspace Approximation Scheme for
 the Tournament Shortest Path Problem
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 There exists an approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
@@ -4830,6 +5302,7 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
 status collapsed
@@ -4843,10 +5316,6 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
 \begin_layout Standard
 \begin_inset Note Note
 status open
@@ -4861,7 +5330,8 @@ fragile
 \end_inset
 
 .
- LyX has the FragileFrame layout for this.
+ \SpecialChar LyX
+ has the FragileFrame layout for this.
 \end_layout
 
 \end_inset
@@ -4884,6 +5354,10 @@ Just a frame with a program code listing
 
 \begin_layout FragileFrame
 This is some program code:
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -4952,10 +5426,24 @@ Summary
 Summary
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Summary
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status collapsed
@@ -4967,6 +5455,10 @@ Summary
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -5036,7 +5528,10 @@ in tournaments is
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -5051,6 +5546,10 @@ Outlook
 \end_inset
 
 
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -5108,15 +5607,30 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection*
 For Further Reading
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 For Further Reading
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status open
@@ -5134,7 +5648,6 @@ beamertemplatebookbibitems
 \end_layout
 
 \begin_layout Bibliography
-\labelwidthstring References
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "Moon1968"
@@ -5195,7 +5708,6 @@ beamertemplatearticlebibitems
 \end_layout
 
 \begin_layout Bibliography
-\labelwidthstring References
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "NickelsenT2002"
@@ -5242,7 +5754,6 @@ Proc.
 \end_layout
 
 \begin_layout Bibliography
-\labelwidthstring References
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "Tantau2004b"
@@ -5302,10 +5813,7 @@ newblock
  In press.
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \start_of_appendix
 \begin_inset ERT
@@ -5331,20 +5839,34 @@ Appendix
 Graphs With Bounded Independence Number
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
+\begin_layout Frame
+\begin_inset Argument 3
 status collapsed
 
 \begin_layout Plain Layout
-
-[label=independence]
+label=independence
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Definition of Independence Number of a Graph
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
 The
 \color none
@@ -5374,7 +5896,19 @@ Tournaments have independence number 1.
  
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Results for Tournaments also Apply to
 \begin_inset Newline newline
 \end_inset
@@ -5382,6 +5916,16 @@ The Results for Tournaments also Apply to
 Graphs With Bounded Independence Number
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 For each
 \begin_inset space ~
@@ -5418,7 +5962,10 @@ at most
 .
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -5451,7 +5998,10 @@ for approximating the shortest path in graphs with independence number at
 
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -5493,21 +6043,36 @@ in graphs with independence number at most
 .
 \end_layout
 
+\end_deeper
 \begin_layout Subsection
 Finding Paths in Undirected Graphs
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
+\begin_layout Frame
+\begin_inset Argument 1
 status collapsed
 
 \begin_layout Plain Layout
+1-2
+\end_layout
+
+\end_inset
 
-<1-2>[label=undirected]
+
+\begin_inset Argument 3
+status collapsed
+
+\begin_layout Plain Layout
+label=undirected
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Complexity of Finding Paths in Undirected Graphs
 \begin_inset Newline newline
 \end_inset
@@ -5515,6 +6080,16 @@ The Complexity of Finding Paths in Undirected Graphs
 Is Party Unknown.
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{undirected}}$
 \end_inset
@@ -5528,6 +6103,10 @@ Is Party Unknown.
 
 \begin_layout Corollary
 For undirected graphs, we can solve
+\begin_inset Separator parbreak
+\end_inset
+
+
 \end_layout
 
 \begin_deeper
@@ -5636,25 +6215,40 @@ the approximation problem in logspace iff ?.
  
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection
 The Approximation Scheme is Optimal
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
+\begin_layout Frame
+\begin_inset Argument 3
 status collapsed
 
 \begin_layout Plain Layout
-
-[label=optimality]
+label=optimality
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Approximation Scheme is Optimal
 \end_layout
 
+\end_inset
+
+
+\begin_inset Separator parbreak
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 Suppose there exists an approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
@@ -5673,6 +6267,9 @@ Suppose there exists an approximation scheme for
 \end_layout
 
 \begin_layout Proof
+\begin_inset Separator parbreak
+\end_inset
+
 
 \end_layout
 
@@ -5738,9 +6335,6 @@ qedhere
 \end_layout
 
 \end_deeper
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \end_body
 \end_document