Reducing an integral flow to $p$ mini flows in a network
$begingroup$
Let $x$ be an integral flow in a given network $R = (G, s, t, c)$, with $v(x) = v_1 + v_2 + cdots + v_p$, where
$v_i in mathbb N∗$, $forall i = 1, p, p > 1$.
Prove that there exists $p$ integral flows $x1, x2,ldots, x_p$
such that $v(x_i) = v_i$,
$forall i = 1, p$ and
$x=sum_{i=1}^n x_i$
$s$-start vertex, $t$-final vertex, $c$-capacity function
So I got this problem to solve and got some instructions like using induction or thinking of a way to solve it by thinking of how $p-1$ affects $p$ but I still can't quite understand how should I start or how to do it. So any advice from you or some kind of lemma to help me in the process will be very appreciated.
graph-theory network-flow
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
$endgroup$
add a comment |
$begingroup$
Let $x$ be an integral flow in a given network $R = (G, s, t, c)$, with $v(x) = v_1 + v_2 + cdots + v_p$, where
$v_i in mathbb N∗$, $forall i = 1, p, p > 1$.
Prove that there exists $p$ integral flows $x1, x2,ldots, x_p$
such that $v(x_i) = v_i$,
$forall i = 1, p$ and
$x=sum_{i=1}^n x_i$
$s$-start vertex, $t$-final vertex, $c$-capacity function
So I got this problem to solve and got some instructions like using induction or thinking of a way to solve it by thinking of how $p-1$ affects $p$ but I still can't quite understand how should I start or how to do it. So any advice from you or some kind of lemma to help me in the process will be very appreciated.
graph-theory network-flow
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
$endgroup$
$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00
add a comment |
$begingroup$
Let $x$ be an integral flow in a given network $R = (G, s, t, c)$, with $v(x) = v_1 + v_2 + cdots + v_p$, where
$v_i in mathbb N∗$, $forall i = 1, p, p > 1$.
Prove that there exists $p$ integral flows $x1, x2,ldots, x_p$
such that $v(x_i) = v_i$,
$forall i = 1, p$ and
$x=sum_{i=1}^n x_i$
$s$-start vertex, $t$-final vertex, $c$-capacity function
So I got this problem to solve and got some instructions like using induction or thinking of a way to solve it by thinking of how $p-1$ affects $p$ but I still can't quite understand how should I start or how to do it. So any advice from you or some kind of lemma to help me in the process will be very appreciated.
graph-theory network-flow
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
$endgroup$
Let $x$ be an integral flow in a given network $R = (G, s, t, c)$, with $v(x) = v_1 + v_2 + cdots + v_p$, where
$v_i in mathbb N∗$, $forall i = 1, p, p > 1$.
Prove that there exists $p$ integral flows $x1, x2,ldots, x_p$
such that $v(x_i) = v_i$,
$forall i = 1, p$ and
$x=sum_{i=1}^n x_i$
$s$-start vertex, $t$-final vertex, $c$-capacity function
So I got this problem to solve and got some instructions like using induction or thinking of a way to solve it by thinking of how $p-1$ affects $p$ but I still can't quite understand how should I start or how to do it. So any advice from you or some kind of lemma to help me in the process will be very appreciated.
graph-theory network-flow
graph-theory network-flow
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
edited Jan 2 at 16:24
Alex Ravsky
43.5k32583
43.5k32583
asked Jan 2 at 10:27
DragomasDragomas
6
asked Jan 2 at 10:27
DragomasDragomas
6
asked Jan 2 at 10:27
DragomasDragomas
6
6
$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00
add a comment |
$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00
$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00
$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00
add a comment |
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$begingroup$
A duplicate of this question.
$endgroup$
– Alex Ravsky
Jan 10 at 23:00