AbstractM. Iri has proved that the maximum rank for a pivotal system of matrices (i.e., combivalence class) equals the minimum term rank. Here this and some of Iri's related results are generalized to matroids. These generalizations are presented using a representation of matroids with (0,1)-matrices. Then, with the aid of matroid basis graphs, these generalizations are restated graph-theoretically. Finally, related results about certain uniform basis graphs are derived
In a recent paper, Bruhn, Diestel, Kriesell and Wollan present four systems of axioms for infinite m...
Tutte associates a V by V skew-symmetric matrix T, having indeterminate entries, with a graph G = (V...
AbstractSeveral graph-theoretic notions applied to matroid basis graphs in the preceding paper are n...
AbstractM. Iri has proved that the maximum rank for a pivotal system of matrices (i.e., combivalence...
AbstractA theorem which establishes a new link between linear algebra and combinatorial mathematics ...
AbstractKishi and Kajitani introduced the concepts of the principal partition of a graph and maximal...
Let P(G) be the set of all positive semidefinite matrices whose graph is G, and msr(G) be the minimu...
AbstractThe maximum rank completion problem is the problem of, given a partial matrix (that is, a ma...
A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of ...
AbstractA graph describes the zero–nonzero pattern of a family of matrices, with the type of graph (...
For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of...
AbstractFor t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest n...
AbstractWe provide a counterexample to a recent conjecture that the minimum rank over the reals of e...
AbstractIn this paper we introduce a new parameter for a graph called the minimum universal rank. Th...
In this paper we introduce a new parameter for a graph called the minimum universal rank. This param...
In a recent paper, Bruhn, Diestel, Kriesell and Wollan present four systems of axioms for infinite m...
Tutte associates a V by V skew-symmetric matrix T, having indeterminate entries, with a graph G = (V...
AbstractSeveral graph-theoretic notions applied to matroid basis graphs in the preceding paper are n...
AbstractM. Iri has proved that the maximum rank for a pivotal system of matrices (i.e., combivalence...
AbstractA theorem which establishes a new link between linear algebra and combinatorial mathematics ...
AbstractKishi and Kajitani introduced the concepts of the principal partition of a graph and maximal...
Let P(G) be the set of all positive semidefinite matrices whose graph is G, and msr(G) be the minimu...
AbstractThe maximum rank completion problem is the problem of, given a partial matrix (that is, a ma...
A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of ...
AbstractA graph describes the zero–nonzero pattern of a family of matrices, with the type of graph (...
For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of...
AbstractFor t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest n...
AbstractWe provide a counterexample to a recent conjecture that the minimum rank over the reals of e...
AbstractIn this paper we introduce a new parameter for a graph called the minimum universal rank. Th...
In this paper we introduce a new parameter for a graph called the minimum universal rank. This param...
In a recent paper, Bruhn, Diestel, Kriesell and Wollan present four systems of axioms for infinite m...
Tutte associates a V by V skew-symmetric matrix T, having indeterminate entries, with a graph G = (V...
AbstractSeveral graph-theoretic notions applied to matroid basis graphs in the preceding paper are n...
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