All Questions
11 questions with no upvoted or accepted answers
10
votes
0
answers
722
views
Fractional Matching version of Hall's Marriage theorem
Let $G=(S,T,E)$ be a bipartite graph, $|S|=|T|$. Then the following are equivalent:
1) there exist a perfect matching in $G$;
2) there exist non-negative weights on edges such that the sum of ...
- 109k
5
votes
0
answers
194
views
A linear optimization problem on a graph
Let $G=(V,E)$ be a finite graph and let $f$ be any positive function defined on the vertices. Put weights on the vertices $v_{i}$, way $w_{i}$ so that $\sum_{i=1}^{n}w_{i}\leq 1$. Assume that every ...
- 2,288
5
votes
0
answers
581
views
When is polytope compatible with network flow?
A linear program is the problem of optimizing an linear objective function within some polytope $A$ over $\mathbf R^n$. My question is motivated by the question of when a linear programming problem ...
- 3,475
2
votes
0
answers
126
views
Unveiling hidden structures
One way to unveil a hidden structure of a undirected graph - given as an adjacency matrix - is to permute the rows and columns until a pattern with a maximal geometrical symmetry is found. (The ...
- 9,720
2
votes
0
answers
177
views
Formulating shortest path as submodular minimization
I'm curious about the general question of whether any combinatorial optimization problem with polynomial time solution can necessarily be reformulated as minimizing a submodular function.
The answer ...
- 21
1
vote
0
answers
62
views
LP Constraints for Bridgeless Cactus Graphs
When trying to determine the optimal bridgeless spanning cactus graph of a weighted, symmetric graph, I got stuck.
What I do not know how to capture, is
the variable number and sizes of the cycles
...
- 13.2k
1
vote
0
answers
60
views
On the defect of a flow network
This problem in graph theory was actually motivated by some problems in Theory of Fractals.
To formulate the problem I need to recall some definitions related to flow network.
A flow network is a ...
- 41.8k
1
vote
0
answers
20
views
Calculating Cost-Optimal 1-Factors in Digraphs
I need to find a cost-optimal 1-factor in a positively weighted, directed, regular graph $G(V,A)$ without antiparallel arcs, i.e. given $$\text{deg}_{\text{in}}(u)=\text{deg}_{\text{in}}(v)=\text{deg}...
- 13.2k
1
vote
0
answers
43
views
a question about probabilities on spaces of digraphs
Let $G$ be a directed graph with fixed nodes $s$ and $t$. Assume that each edge $e$ in the graph comes with a number $n(e)\in[0,1]$.
We consider probability spaces $S$ whose points are directed ...
- 61
0
votes
0
answers
40
views
Subtour-gluing constraints for ILP formulation of TSPs
If one doesn't want to introduce additional variables to the ILP of a TSP instance, one has to add exponentially many so-called subtour-elimination constraints; in practical calculations subtour-...
- 13.2k
0
votes
0
answers
99
views
Is this Graph Iteration Already Known?
When attempting to set up an ILP formulation for a weight-minimal cubic spanning tree (i.e. one with vertex degrees either 1 or 3) I needed connectivity constraint, but misremembered the contents of ...
- 13.2k