A
\color red
tournament
-\color default
+\color inherit
is a
\end_layout
A
\color red
graph
-\color default
+\color inherit
\begin_inset Formula $G=(V,E)$
\end_inset
, a
\color red
source
-\color default
+\color inherit
\begin_inset Formula $s\in V$
\end_inset
and a
\color red
target
-\color default
+\color inherit
\begin_inset Formula $t\in V$
\end_inset
A
\color red
maximum distance
-\color default
+\color inherit
\InsetSpace ~
\begin_inset Formula $d$
An
\color red
approximation ratio
-\color default
+\color inherit
\begin_inset Formula $r>1$
\end_inset
\end_inset
-\color default
+\color inherit
contain all triples
\begin_inset Formula $(T,s,t)$
\end_inset
\end_inset
-\color default
+\color inherit
contain all tuples
\begin_inset Formula $(T,s,t,d)$
\end_inset
\end_inset
-\color default
+\color inherit
gets as input
\end_layout
Tournament
\color red
reachability
-\color default
+\color inherit
is in
\color red
\end_inset
-\color default
+\color inherit
.
\end_layout
There exists a
\color red
logspace approximation scheme
-\color default
+\color inherit
for
\color red
approximating
-\color default
+\color inherit
shortest paths in tournaments.
\end_layout
Finding
\color red
shortest paths
-\color default
+\color inherit
in tournaments is
\color red
\end_inset
-complete
-\color default
+\color inherit
.
\end_layout
The
\color red
independence number
-\color default
+\color inherit
\begin_inset Formula $\alpha(G)$
\end_inset
,
\color red
reachability
-\color default
+\color inherit
in graphs with independence number
\newline
at most\InsetSpace ~
, there exists a
\color red
logspace approximation scheme
-\color default
+\color inherit
for approximating the shortest path in graphs with independence number
at most\InsetSpace ~
, finding the
\color red
shortest path
-\color default
+\color inherit
in graphs with independence number at most\InsetSpace ~
\begin_inset Formula $k$
\end_inset
-complete
-\color default
+\color inherit
.
\end_layout