fix definition of path and add references to state graphs and bridges

book.tex

@@ -104,11 +104,17 @@
 \include{chapter14}
 \include{chapter16}
 %\include{chapter20}
+\chapter{State Graphs}
+Please watch the video about state graphs.
+The video should be linked on the graph overview site, but please push Johannes
+to fix the link here too.
 
 \part{Advanced topics}
 \include{chapter15}
 \include{chapter17}
 \include{chapter18}
+\chapter{Bridges and Articulation Points}
+Please read our wiki: \url{https://soi.ch/wiki/bridges-articulationpoints/}
 \include{chapter19}
 
 % \part{Advanced topics}

chapter11.tex

@@ -29,6 +29,10 @@ the number of edges.
 The nodes are numbered
 using integers $1,2,\ldots,n$.
 
+Note: at SOI we usually say \key{vertex} (plural \key{vertices}) instead of \key{node}.
+Vertex and node can be used interchangeably.
+We also like to number the vertices 0-based as $0,1,\ldots,n-1$.
+
 For example, the following graph consists of 5 nodes and 7 edges:
 
 \begin{center}
@@ -51,9 +55,11 @@ For example, the following graph consists of 5 nodes and 7 edges:
 
 \index{path}
 
-A \key{path} leads from node $a$ to node $b$
+A \key{walk} leads from node $a$ to node $b$
 through edges of the graph.
-The \key{length} of a path is the number of
+A \key{path} is a walk where each node appears
+at most once in the path.
+The \key{length} of a path (or a walk) is the number of
 edges in it.
 For example, the above graph contains
 a path $1 \rightarrow 3 \rightarrow 4 \rightarrow 5$
@@ -84,12 +90,10 @@ from node 1 to node 5:
 
 \index{cycle}
 
-A path is a \key{cycle} if the first and last
-node is the same.
+A \key{cycle} is a walk where the first and last
+node is the same, and every other vertex appears at most once.
 For example, the above graph contains
 a cycle $1 \rightarrow 3 \rightarrow 4 \rightarrow 1$.
-A path is \key{simple} if each node appears
-at most once in the path.
 
 
 %