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

This commit is contained in:
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.pdf
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book.tex
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@ -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}

16
chapter11.tex
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@ -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.
%