Perfect 0 , + 1 Matrices *
نویسنده
چکیده
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 253:299-309 (1997) 0 Elsevier Science Inc., 1997 0024-3795/97/$17.00 655 Avenue of the Americas, New York, NY 10010 SSDI 0024-3795@6)00773-3 300 MICHELE CONFORTI ET AL.
منابع مشابه
On 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 کاملMatrix partitions of perfect graphs
Given a symmetric m by m matrix M over 0, 1, ∗, the M -partition problem asks whether or not an input graph G can be partitioned into m parts corresponding to the rows (and columns) of M so that two distinct vertices from parts i and j (possibly with i = j) are nonadjacent if M(i, j) = 0, and adjacent if M(i, j) = 1. These matrix partition problems generalize graph colourings and homomorphisms,...
متن کاملInvestigation of Perfect Ternary Arrays PTA ( 60 , 25 )
Perfect ternary arrays are closely related to difference sets and group invariant weighing matrices. A previous paper by one of the authors demonstrated strong restrictions on difference sets with parameters (120, 35, 10). A perfect ternary array with energy 25 and order 60 – PTA(60,25) – would obey an equation analogous to the difference set equation for (120, 35, 10). A perfect ternary array ...
متن کاملEla on Perfect Conditioning of Vandermonde Matrices on the Unit Circle∗
Let K,M ∈ N with K < M , and define a square K × K Vandermonde matrix A = A τ,−→n with nodes on the unit circle: Ap,q = exp (−j2πpnqτ/K) ; p, q = 0, 1, ...,K − 1, where nq ∈ {0, 1, ...,M − 1} and n0 < n1 < .... < nK−1. Such matrices arise in some types of interpolation problems. In this paper, necessary and sufficient conditions are presented on the vector −→n so that a value of τ ∈ R can be fo...
متن کاملOn perfect conditioning of Vandermonde matrices on the unit circle
Let K,M ∈ N with K < M , and define a square K × K Vandermonde matrix A = A τ,−→n with nodes on the unit circle: Ap,q = exp (−j2πpnqτ/K) ; p, q = 0, 1, ...,K − 1, where nq ∈ {0, 1, ...,M − 1} and n0 < n1 < .... < nK−1. Such matrices arise in some types of interpolation problems. In this paper, necessary and sufficient conditions are presented on the vector −→n so that a value of τ ∈ R can be fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003