Zero-one matrices without consecutive ones

Consecutive ones Block for Symmetric Matrices

We show that a cubic graph G with girth g(G) ≥ 5 has a Hamiltonian Circuit if and only if the matrix A+ I can be row permuted such that each column has at most 2 blocks of consecutive 1’s, where A is the adjacency matrix of G, I is the unit matrix, and a block can be consecutive in circular sense, i.e., the first row and the last row are viewed as adjacent rows. Then, based on this necessary an...

A new characterization of matrices with the consecutive ones property

We consider the following constraint satisfaction problem: Given a set F of subsets of a finite set S of cardinality n, and an assignment of intervals of the discrete set {1, . . . , n} to each of the subsets, does there exist a bijection f : S → {1, . . . , n} such that for each element of F, its image under f is same as the interval assigned to it. An interval assignment to a given set of sub...

Consecutive ones matrices for multi-dimensional orthogonal packing problems

The multi-dimensional orthogonal packing problem (OPP) is a well studied optimization problem [3,9]. Given a set of items with rectangular shapes, the problem is to decide whether there is a non-overlapping packing of these items in a rectangular bin. Rotation of items is not allowed. Fekete and Schepers introduced a tuple of interval graphs as data structures to store a feasible packing, and g...

A Loopless Generation of Bitstrings without p consecutive ones

Let F (p) n be the set of all n-length bitstrings such that there are no p consecutive 1s. F (p) n is counted with the pth order Fibonacci numbers and it may be regarded as the subsets of {1, 2, ..., n} without p consecutive elements and bitstrings in F (p) n code a particular class of trees or compositions of an integer. In this paper we give a Gray code for F (p) n which can be implemented in...

Consecutive Ones Property