AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k-connected. It is conjectured that every minimally k-connected matroid with at least 2(k−1) elements has a cocircuit of size k. We resolve the conjecture almost affirmatively for the case k=4 by finding the unique counterexample; and for each k⩾5, we prove that there exists a counterexample to the conjecture with 2k+1 elements
In this paper we derive several results for connected matroids and use these to obtain new results f...
AbstractWe prove that, for any positive integers k, n, and q, if M is a simple matroid that has neit...
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...
AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
By a well-known result of Tutte, if e is an element of a connected matroid M, then either the deleti...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
Halin proved that every minimally $k$-connected graph has a vertex of degree $k$. More generally, do...
AbstractLemos and Oxley proved that if M is a connected matroid with |E(M)|⩾3r(M), then M has a circ...
AbstractWe give a lower bound on the number of edges meeting some vertex of degree k in terms of the...
Let N be a matroid with k connected components and M be a minor-minimal connected matroid having N a...
In this paper we derive several results for connected matroids and use these to obtain new results f...
AbstractWe prove that, for any positive integers k, n, and q, if M is a simple matroid that has neit...
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...
AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such th...
By a well-known result of Tutte, if e is an element of a connected matroid M, then either the deleti...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
Halin proved that every minimally $k$-connected graph has a vertex of degree $k$. More generally, do...
AbstractLemos and Oxley proved that if M is a connected matroid with |E(M)|⩾3r(M), then M has a circ...
AbstractWe give a lower bound on the number of edges meeting some vertex of degree k in terms of the...
Let N be a matroid with k connected components and M be a minor-minimal connected matroid having N a...
In this paper we derive several results for connected matroids and use these to obtain new results f...
AbstractWe prove that, for any positive integers k, n, and q, if M is a simple matroid that has neit...
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...
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