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

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Johannes Kapfhammer 2021-02-10 18:41:16 +01:00
parent 55a61a0050
commit 1cbaab8e46
3 changed files with 16 additions and 6 deletions
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book.tex
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@ -104,11 +104,17 @@
\include{chapter14} \include{chapter14}
\include{chapter16} \include{chapter16}
%\include{chapter20} %\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} \part{Advanced topics}
\include{chapter15} \include{chapter15}
\include{chapter17} \include{chapter17}
\include{chapter18} \include{chapter18}
\chapter{Bridges and Articulation Points}
Please read our wiki: \url{https://soi.ch/wiki/bridges-articulationpoints/}
\include{chapter19} \include{chapter19}
% \part{Advanced topics} % \part{Advanced topics}

16
chapter11.tex
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@ -29,6 +29,10 @@ the number of edges.
The nodes are numbered The nodes are numbered
using integers $1,2,\ldots,n$. 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: For example, the following graph consists of 5 nodes and 7 edges:
\begin{center} \begin{center}
@ -51,9 +55,11 @@ For example, the following graph consists of 5 nodes and 7 edges:
\index{path} \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. 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. edges in it.
For example, the above graph contains For example, the above graph contains
a path $1 \rightarrow 3 \rightarrow 4 \rightarrow 5$ a path $1 \rightarrow 3 \rightarrow 4 \rightarrow 5$
@ -84,12 +90,10 @@ from node 1 to node 5:
\index{cycle} \index{cycle}
A path is a \key{cycle} if the first and last A \key{cycle} is a walk where the first and last
node is the same. node is the same, and every other vertex appears at most once.
For example, the above graph contains For example, the above graph contains
a cycle $1 \rightarrow 3 \rightarrow 4 \rightarrow 1$. a cycle $1 \rightarrow 3 \rightarrow 4 \rightarrow 1$.
A path is \key{simple} if each node appears
at most once in the path.
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