# Is there an upper bound for fill-ins for indefinite triangular factorization?

For $A=LU$, or $A=LDL^T$ factorization, bandwidth is preserved when there is no pivoting. This is true even for indefinite A, see question. However, when there is pivoting band structure is destroyed, so fill-ins can occur outside the band. I am curious if there is any pivoting that can still preserve sparsity for the factors within some bounds.