diff --git a/book.pdf b/book.pdf index 79eec8d..d33718b 100644 Binary files a/book.pdf and b/book.pdf differ diff --git a/book.tex b/book.tex index 1406673..c25d5b3 100644 --- a/book.tex +++ b/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} diff --git a/chapter11.tex b/chapter11.tex index efa605d..e093129 100644 --- a/chapter11.tex +++ b/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. %