Title: Theory / Unimportant / CS / Fundamental / Graph / Bondy - Murty / 07 flows
Tags: récupéré

Name: A network
Definition: \(D\) the underlying digraph
Page: 157
Chapter: 7
Section: 1
Definition2: \(x\in V(D)\) a source, \(y\in V(D)\) a sink
Conjdef: The tuple
Definition4: \(c:A(D)\to\mathbb [0,+\infty]\) the capacity function
Denoted by: \(N(x,y)\)

Name: The capacity of \(a\)
Definition: \(c(a)\)
Page: 157
Chapter: 7
Section: 1
Variables: \(N(x,y)\) a network
\(a\in A(N)\)

Question: How to deal with network with multiple sources ?
Answer: add a single source \(s\), and for each old sources \(s'\), add an edge from \(s\) to \(s'\) with capacity \(\infty\)
Page: 158
Chapter: 7
Section: 1
Index: 3
Kind: Ex

Definition: \(\sum _{a\in S}f(a)\)
Page: 158
Chapter: 7
Section: 1
Variables: \(N(x,y)\) a network
\(f:A(N)\)
\(S\subseteq A(N)\)
Notation: \(f(S)\)

Definition: \(f^\pm(\partial ^\pm(X))\)
Page: 158
Chapter: 7
Section: 1
Variables: \(N(x,y)\) a network
\(f:A(N)\)
\(X\subseteq V(N)\)
Notation: \(f^\pm(X)\)