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 is itself a all 1 submatrix. We differentiate two parts of a clique as a major part in row-view of the matrix and a minor part in column-view. A clique is an extreme maximal one if and only if it satisfies: (1) no other clique has bigger cardinality with major part than that of it; (2) if with the same major cardinality, then no other clique has bigger cardinality with minor part than that of it; (3) the minor cardinality is not less than a specified value s.

Extreme maximal bicliques is very rare by experimental results. However, we do not know what relation between the number of extreme maximal bicliques and n,m.

**The problem is how many extreme maximal bicliques are in an n*m 0-1 matrix at most**.

An example as a 4*4 matrix below, if s=2, then the row 1,2,3 and the column 1,2 make an extreme biclique with major cardinality 3 minor cardinality 2, and there are only 2 such bicliques in the matrix.

## 1 1 1 1

## 1 1 0 0

## 1 1 0 1

## 1 0 0 1

For an n*m 0-1 matrix, if the size of so-called extreme maximal biclique (EMB) is 1*1, then there are at most min(n,m) EMBs in the matrix. We can construct such case matrix with the most many EMBs as below:

## 1 0 0 0 0 0 0 ......

## 0 1 0 0 0 0 0

## 0 0 1 0 0 0 0

## 0 0 0 1 0 0 0

## ......

And **I guess that it holds that there are at most max(n,m) EMBs in an n*m 0-1 matrix**.