Showing papers by "Richard A. Brualdi published in 1993"
TL;DR: The incidence coloring number turns out to be the strong chromatic index of an associated bipartite graphs all of whose cycle lengths are divisible by 4.
125 citations
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TL;DR: It is shown that these greedy codes are linear and a special case of this algorithm gives the lexicodes, thereby providing a proof of their linearity which is independent of game theory.
70 citations
TL;DR: The lower bound on the dimension of linear spaces of Toeplitz matrices is determined which guarantees that it contains a matrix with rank at least equal to a specified number r .
19 citations
TL;DR: Conditional sign-solvable linear systems were introduced by as mentioned in this paper, where they relax the definition of sign-satisfiability so as not to require that each linear system with the same sign pattern as [email protected] = b has a solution.
6 citations
TL;DR: In this paper, the structure-rank of a matrix is defined as the largest rank of a submatrix which lies within a specified structure and characterized those structures avoiding the main diagonal for which a matrix and its inverse have the same structure rank.
5 citations
Proceedings Article•
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TL;DR: In this paper, the authors define a greedy algorithm for constructing a code of minimum distance at least d. They show that these greedy codes are linear and construct a parity check matrix for them.
Abstract: Given an ordered basis of F/sup n//sub 2/ and an integer d, we define a greedy algorithm for constructing a code of minimum distance at least d. We show that these greedy codes are linear and construct a parity check matrix for them. A special case of this algorithm gives the lexicodes, thereby providing a proof of their linearity which is independent of game theory. For ordered bases which have a triangular form we are able to give a lower bound on the dimension of greedy codes. Some greedy codes are better than lexicodes.
4 citations
TL;DR: In this paper, the dimension of the binary vector space which is spanned by the characteristic vectors of perfect matchings of a matching-covered bipartite graph was determined, and it was shown that the cutsets of G are those sets F of edges such that ∣F⋂M∣ has the same parity for every perfect matching M of G.
Abstract: Let G be a matching-covered, connected bipartite graph. We determine the dimension of the binary vector space which is spanned by the characteristic vectors of perfect matchings of G. We then show that the cutsets of G are those sets F of edges such that ∣F⋂M∣ has the same parity for every perfect matching M of G.
3 citations
TL;DR: Brualdi as discussed by the authors is the author of the text Introductory Combinatorics (Eisevier Science, second edition 1991) and author with H. J. Ryser of the monograph Combinatorial Matrix Theory (Cambridge University Press, 1991).
Abstract: Richard A. Brualdi is Professor of Mathematics at the Univer? sity of Wisconsin in Madison, where he has taught since 1965. He is the author of the text Introductory Combinatorics (Eisevier Science, second edition 1991) and author with H. J. Ryser of the monograph Combinatorial Matrix Theory (Cambridge University Press, 1991). He serves on the editorial boards of several journals, and is editor-in-chief of Linear Algebra and Its Applica? tions. His research interests lie primarily in the interface of combinatorics/graph theory and linear algebra.
2 citations