AbstractA connected matroid M is called a critically connected matroid if the deletion of any one element from M results in a disconnected matroid. We show that a critically connected matroid of rank n, n≥3, can have at most 2n−2 elements. We also show that a critically connected matroid of rank n on 2n−2 elements is isomorphic to the forest matroid of K2, n−2
The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and ...
Tutte proved that if e is an element of a 3-connected matroid M such that neither M\e nor M/e is 3-c...
Abstract. A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid ...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractLet n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this...
AbstractIt is a well-known result of Tutte that, for every element x of a connected matroid M, at le...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
Connectivity is a fundamental tool for matroid theorists, which has become increasingly important in...
AbstractDing, Oporowski, Oxley, and Vertigan proved that, for alln⩾3, there is an integerN(n) such t...
Dirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected graph G has...
AbstractIt is shown that loopless transveral matroids have critical exponent at most 2
Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say tha...
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the depen...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and ...
Tutte proved that if e is an element of a 3-connected matroid M such that neither M\e nor M/e is 3-c...
Abstract. A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid ...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractLet n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this...
AbstractIt is a well-known result of Tutte that, for every element x of a connected matroid M, at le...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
Connectivity is a fundamental tool for matroid theorists, which has become increasingly important in...
AbstractDing, Oporowski, Oxley, and Vertigan proved that, for alln⩾3, there is an integerN(n) such t...
Dirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected graph G has...
AbstractIt is shown that loopless transveral matroids have critical exponent at most 2
Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say tha...
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the depen...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and ...
Tutte proved that if e is an element of a 3-connected matroid M such that neither M\e nor M/e is 3-c...
Abstract. A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid ...
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