**2**

votes

**1**answer

200 views

### Solving assignment problem using Hungarian method vs min cost max flow problem

The traditional solution for the assignment problem is the Hungarian method - it's complexity is O(V^4) or O(V^3) if using Edmonds method.
However, it can also be reduced to a min cost max flow ...

**4**

votes

**0**answers

148 views

### Bounds on numbers of matchings of given sizes in bipartite graphs

I am interested in the following question:
For which sets ${m_1,\ldots m_k}$ of positive integers do there exist bipartite graphs having exactly $m_i$ matchings of size $i$ for each $1\leq i \leq k$, ...

**2**

votes

**0**answers

72 views

### Minimum number of perfect matchings in a regular bipartite graph

Is there a lower bound on the number of perfect matchings in a $k$-regular bipartite graph?
One can use Hall's marriage theorem and induction on $k$ to derive the lower bound of $k$. I can't come up ...

**2**

votes

**0**answers

64 views

### Characterize the equivalence class of bipartite graphs obtained from each other by elementary row operations on their adjacency matrices

Let $M$ be an $m\times n$ matrix real matrix. Let $G$ be a bipartite graph, with partitions $A$ and $B$, such that $|A|=m$ and $|B|=n$. A node $i\in A$ is linked to a node $j\in B$ if and only if ...

**2**

votes

**0**answers

111 views

### Bipartite independence number

Consider a balanced bipartite graph $G=(U,V,E)$, i.e., a bipartite graph with $|U|=|V|$. An independent set $I$ of $G$ is balanced if $|I \cap U| = |I \cap V|$.
The bipartite independence number of ...

**2**

votes

**0**answers

149 views

### Structure of almost all bipartite graphs

I am studying some properties related to bipartite graphs and it would be useful for me to know if there is anything known about the structure of almost all bipartite graphs. For example, is it true ...

**1**

vote

**0**answers

73 views

### Details about Kelman's equivalent form of Barnette's conjecture

Barnette's conjecture states that every cubic planar bipartite 3-connected graph admits Hamiltonian cycles.
Kelman claims that this conjecture is equivalent to a stronger one, which imposes some ...

**1**

vote

**0**answers

91 views

### How many extreme maximal cliques are in an n*m 0-1 matrix?

We can use an n*m 0-1 matrix to denote a bipartite graph. Mining maximal bicliques in such matrix is an open problem.
The extreme maximal clique is a special maximal clique. A clique in such matrix ...