UserGuide.lyx: fix some typographic issues spotted by Mike

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

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 85e0af7f60ab5b7dbd655dcd417b8164c69e41ed..9d51a378bcbba090a36eeb2befa4b16c9d367482 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -262,10 +262,6 @@ Outline
 \end_inset
 
 
-\begin_inset Separator latexpar
-\end_inset
-
-
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 \begin_deeper
@@ -366,17 +362,10 @@ Tournaments Consist of Jousts Between Knights
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
 \begin_layout Columns
-\begin_inset Separator latexpar
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-
 
 \end_layout
 
@@ -566,10 +555,6 @@ What is a Tournament?
 \end_inset
 
 
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-
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 \begin_deeper
@@ -616,7 +601,7 @@ In every joust one knight wins.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
 
@@ -633,17 +618,10 @@ Tournaments are Complete Directed Graphs
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
 \begin_layout Columns
-\begin_inset Separator latexpar
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 \end_layout
 
@@ -871,10 +849,6 @@ tournament
  
 \color inherit
 is a
-\begin_inset Separator latexpar
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-
-
 \end_layout
 
 \begin_deeper
@@ -894,7 +868,7 @@ any two different vertices.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
 
@@ -921,10 +895,6 @@ Tournaments Arise Naturally in Different Situations
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -939,10 +909,6 @@ Applications in Ordering Theory
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
-
 \end_layout
 
 \begin_deeper
@@ -957,7 +923,7 @@ The comparison relation may be cyclic, however.
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
 
@@ -974,10 +940,6 @@ Applications in Sociology
 \end_inset
 
 
-\begin_inset Separator latexpar
-\end_inset
-
-
 \end_layout
 
 \begin_deeper
@@ -992,7 +954,7 @@ Reviewers decide for any two candidates whom they prefer.
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
 
@@ -1009,10 +971,6 @@ Applications in Structural Complexity Theory
 \end_inset
 
 
-\begin_inset Separator latexpar
-\end_inset
-
-
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 \begin_deeper
@@ -1053,10 +1011,6 @@ status open
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -1193,10 +1147,6 @@ the Approximation Problem
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -1333,10 +1283,6 @@ status open
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -1351,10 +1297,6 @@ t,onlytextwidth
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -1428,10 +1370,6 @@ Example Input
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -1821,10 +1759,6 @@ Example Output
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2051,10 +1985,6 @@ status open
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2069,10 +1999,6 @@ Variants of Path Finding Problems
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -2288,10 +2214,6 @@ Logspace Turing Machines
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2460,7 +2382,7 @@ end{pgfpicture}
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -2477,10 +2399,6 @@ Logspace Turing Machines Are Quite Powerful
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2495,10 +2413,6 @@ Deterministic logspace machines can compute
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2530,10 +2444,6 @@ Non-deterministic logspace machines can compute
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -2552,7 +2462,7 @@ satisfiability with two literals per clause.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -2589,10 +2499,6 @@ The Complexity Class Hierarchy
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-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -2981,7 +2887,7 @@ end{pgfpicture}
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -3014,10 +2920,6 @@ Limit the Circuit Depth
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3057,10 +2959,6 @@ t
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3083,10 +2981,6 @@ Circuit Class
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3103,9 +2997,6 @@ unbounded fan-in
 
 \end_deeper
 \begin_layout Examples
-\begin_inset Separator latexpar
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-
 
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@@ -3148,10 +3039,6 @@ Circuit Class
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3168,9 +3055,6 @@ bounded fan-in
 
 \end_deeper
 \begin_layout Examples
-\begin_inset Separator latexpar
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@@ -3220,10 +3104,6 @@ Circuit Class
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-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -3240,9 +3120,6 @@ bounded fan-in
 
 \end_deeper
 \begin_layout Examples
-\begin_inset Separator latexpar
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-
 
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@@ -3289,10 +3166,6 @@ Are Equally Difficult
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3318,10 +3191,6 @@ Are Equally Difficult
 
 \begin_layout Corollary
 For directed graphs, we can solve
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3387,10 +3256,6 @@ But Not Trivial
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3410,7 +3275,7 @@ But Not Trivial
 \end_layout
 
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -3464,10 +3329,6 @@ Definition of the Tournament Reachability Problem
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -3489,10 +3350,6 @@ contain all triples
 \end_inset
 
  such that
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3526,7 +3383,7 @@ there exists a path from
 \end_deeper
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -3543,10 +3400,6 @@ The Tournament Reachability Problem is Very Easy
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -3572,10 +3425,6 @@ Implications
 \end_inset
 
 
-\begin_inset Separator latexpar
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 \begin_deeper
@@ -3640,10 +3489,6 @@ the Distance Problem
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -3665,10 +3510,6 @@ contain all tuples
 \end_inset
 
  such that 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3706,7 +3547,7 @@ the distance of
 \end_deeper
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 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -3723,10 +3564,6 @@ The Tournament Distance Problem is Hard
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -3792,7 +3629,7 @@ in logarithmic space, iff
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
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@@ -3813,10 +3650,6 @@ Proof That
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -3847,10 +3680,6 @@ t,onlytextwidth
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -3895,10 +3724,6 @@ Reduce
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-\begin_inset Separator latexpar
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 \begin_deeper
@@ -3967,7 +3792,7 @@ Query:
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -3994,10 +3819,6 @@ status open
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-\begin_inset Separator latexpar
-\end_inset
-
-
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 \begin_deeper
@@ -5153,10 +4974,6 @@ Approximators Compute Paths that Are Nearly As Short As a Shortest Path
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-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -5174,10 +4991,6 @@ approximation scheme for
  
 \color inherit
 gets as input
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -5224,7 +5037,7 @@ a path from
 \end_deeper
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -5245,10 +5058,6 @@ the Tournament Shortest Path Problem
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-\begin_inset Separator latexpar
-\end_inset
-
-
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 \begin_deeper
@@ -5354,10 +5163,6 @@ Just a frame with a program code listing
 
 \begin_layout FragileFrame
 This is some program code:
-\begin_inset Separator latexpar
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 \begin_deeper
@@ -5437,10 +5242,6 @@ Summary
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -5455,10 +5256,6 @@ Summary
 \end_inset
 
 
-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -5529,7 +5326,7 @@ in tournaments is
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -5546,10 +5343,6 @@ Outlook
 \end_inset
 
 
-\begin_inset Separator latexpar
-\end_inset
-
-
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 \begin_deeper
@@ -5624,10 +5417,6 @@ For Further Reading
 \end_inset
 
 
-\begin_inset Separator latexpar
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 \begin_deeper
@@ -5860,10 +5649,6 @@ Definition of Independence Number of a Graph
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -5898,7 +5683,7 @@ Tournaments have independence number 1.
 
 \end_deeper
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -5919,10 +5704,6 @@ Graphs With Bounded Independence Number
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -5963,7 +5744,7 @@ at most
 \end_layout
 
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -5999,7 +5780,7 @@ for approximating the shortest path in graphs with independence number at
 \end_layout
 
 \begin_layout Standard
-\begin_inset Separator parbreak
+\begin_inset Separator plain
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@@ -6083,10 +5864,6 @@ Is Party Unknown.
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-\begin_inset Separator latexpar
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-
-
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 \begin_deeper
@@ -6103,10 +5880,6 @@ Is Party Unknown.
 
 \begin_layout Corollary
 For undirected graphs, we can solve
-\begin_inset Separator latexpar
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 \begin_deeper
@@ -6242,10 +6015,6 @@ The Approximation Scheme is Optimal
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-\begin_inset Separator latexpar
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-
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 \begin_deeper
@@ -6267,9 +6036,6 @@ Suppose there exists an approximation scheme for
 \end_layout
 
 \begin_layout Proof
-\begin_inset Separator latexpar
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-
 
 \end_layout