منابع مشابه
(0, ±1) Ideal Matrices
A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of nding a satisfactory characterization of those matrices which are minimally non-ideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally non-ideal matrices. ...
متن کاملNotes on "Ideal 0, 1 matrices" by Cornuéjols and Novick
In 1994, Cornuéjols and Novick published a classification of ideal and minimally non ideal circulant clutters. One of their main results for doing so relates contractions of these clutters, simple directed cycles in an appropriate graph, and algebraic conditions. The purpose of this paper is twofold: to correct a small inaccuracy of the necessity of the algebraic conditions in the original proo...
متن کاملPerfect 0 , + 1 Matrices *
Perfect graphs and perfect 0,l matrices are well studied in the literature. Here we introduce perfect 0, f 1 matrices. Our main result is a characterization of these matrices in terms of a family of perfect 0,l matrices. 0 Elsevim Science Inc., 1997 * This work was supported in part by NSF grants DMI-9424348 and DMS-9509581, and by ONR grant NOOO14-89-J-1063. LINEAR ALGEBRA AND ITS APPLZCATIONS...
متن کاملOn perfect 0, +/- 1 matrices,
Perfect 0,±1 matrices were introduced recently in [5] as a generalization of the well-studied class of perfect 0, 1 matrices. In this paper we provide a characterization of perfect 0,±1 matrices in terms of an associated perfect graph which one can build in O(nm) time, where m × n is the size of the matrix. We also obtain an algorithm of the same time complexity, for testing the irreducibility ...
متن کاملTotally Nonnegative (0, 1)-Matrices
We investigate (0, 1)-matrices which are totally nonnegative and therefore which have all of their eigenvalues equal to nonnegative real numbers. Such matrices are characterized by four forbidden submatrices (of orders 2 and 3). We show that the maximum number of 0s in an irreducible (0, 1)-matrix of order n is (n − 1) and characterize those matrices with this number of 0s. We also show that th...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1994
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1009