From 1cbaab8e4699d751fb7e3304c5ec5f5b4729abf8 Mon Sep 17 00:00:00 2001 From: Johannes Kapfhammer Date: Wed, 10 Feb 2021 18:41:16 +0100 Subject: [PATCH] fix definition of path and add references to state graphs and bridges --- book.pdf | Bin 315920 -> 322196 bytes book.tex | 6 ++++++ chapter11.tex | 16 ++++++++++------ 3 files changed, 16 insertions(+), 6 deletions(-) diff --git a/book.pdf b/book.pdf index 79eec8da7cef6ad315c6d98867d98058e2790163..d33718bcae4b8f159337874b386ff1a8d9d144bd 100644 GIT binary patch delta 177215 zcmZsiV{l+W*Pti1F|lpi=EQa~v5iS`lT2*ewr$%sC$^J`cHaGVw`!~2e_i+1ITzK{ z{XFMX#}=X`E}@~4D~d_bGc&NmlFu#;MFs1Zjf}z(@uz`Sba3nF5>u!3;M zp`d|ram|3bX-@N}Yf?Bsyfv#J%q5Yx@9I6g)qukcli@8H0-xUqyA{ z2P_eHO$0_@`mhS@$5kCcm2*ij;g_P)8n3X4C_`;{@x;Q7_%a8j5%IFhmL=Qe9-9oz z)!FZTV-n;@&Kev&1+n+2zq80lCC}ejUR6yDY5>B4j26C4wC<#9TMfcon!6IwP1%Y3o}Q-(PZ(QE)qApwqxn z5gPH%q4?;*WTK<8)M#yW)Y?bnm?Z7%6XIOtFtI$VGwib82eE86Ja2TWF32!Pvq=2A zwDbiS-}mVK5=nJ+!eIPU&DAST(Wo3{5K#%*!3cn}J#O3ddAVR2+h5ebHV$8S#QArV zx^m0QYR<0j*WJ8!lW8v`T(?bA!Nmrs{R^|x4*wrs{EAdE)-tI-+uy5|2mJalR?Yz`)7; zvRed1I;KnQ-~Rv)IR+@)?O<(0{idg5>dQ-VPzg9efhwNhQl`AI#swJ}GHV@*Y1+@( zL%W)%kEm0V0cMB?YJ&Y-Z;V|o&C?@t?9NE==Agpc#|8?T1*f-j54yhuX|BYvD#5v$ zid<^^8Rfi77Lv*-ym;J(4hAKieqhtcTN^>*Onx

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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. %