Given a flow network $(G,\mu,s,t)$. I am thinking about the following statement.
A flow $f$ is maximum $\Leftrightarrow$ $\exists$ an empty $s$-$t$ cut
I know "$\Rightarrow$ is correct, but also "$\Leftarrow$"?
2026-03-27 16:39:14.1774629554
A flow $f$ is maximum $\Leftrightarrow$ $\exists$ an empty $s$-$t$ cut
49 Views Asked by user187786 https://math.techqa.club/user/user187786/detail AtRelated Questions in GRAPH-THEORY
- characterisation of $2$-connected graphs with no even cycles
- Explanation for the static degree sort algorithm of Deo et al.
- A certain partition of 28
- decomposing a graph in connected components
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Fake induction, can't find flaw, every graph with zero edges is connected
- Triangle-free graph where every pair of nonadjacent vertices has exactly two common neighbors
- Inequality on degrees implies perfect matching
- Proving that no two teams in a tournament win same number of games
- Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one
Related Questions in DUALITY-THEOREMS
- Computing Pontryagin Duals
- How to obtain the dual problem?
- Optimization problem using Fenchel duality theorem
- Deriving the gradient of the Augmented Lagrangian dual
- how to prove that the dual of a matroid satisfies the exchange property?
- Write down the dual LP and show that $y$ is a feasible solution to the dual LP.
- $\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?
- Group structure on the dual group of a finite group
- Proving that a map between a normed space and its dual is well defined
- On the Hex/Nash connection game theorem
Related Questions in NETWORK-FLOW
- Flow graph force flow to "move" together
- min cost flow in offline bipartite graph problem
- Looking for some information on applications of integer linear programming
- Linear Programming Primal-Dual tough question
- question about the min cut max flow theorm
- Flows: Graph Theory/Groups, Empty Set
- Max number of vertex disjoint S-T paths in time O(VE)
- Minimum cut on a directed graph with negative term
- Minimum capacity cut reduction from digraph with two edge weight sets
- Dual Of Integer Network Formulation
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?