Add to ORKGDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected graph G has at least ((n-1)|V(G)|-2n)/(2n-1) vertices of degree n. This paper determines the graphs which are extremal with respect to these two results and, in addition, establishes a similar extremal result for minimally connected matroids. © 1982
AbstractDing, Oporowski, Oxley, and Vertigan proved that, for alln⩾3, there is an integerN(n) such t...
AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k...
We refine a property of $2$-connected graphs described in the classical paper of Dirac from 1952 and...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
AbstractWe give a lower bound on the number of edges meeting some vertex of degree k in terms of the...
In this paper we derive several results for connected matroids and use these to obtain new results f...
By a well-known result of Tutte, if e is an element of a connected matroid M, then either the deleti...
Let G be a (multi)graph of order n and let u, v be vertices of G. The maximum number of internally ...
Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say tha...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractThe structure of connected graphs of given size and order that have minimal algebraic connec...
Halin proved that every minimally $k$-connected graph has a vertex of degree $k$. More generally, do...
The edge-connectivity l of a connected graph is the minimum number of edges whose deletion produc...
AbstractDing, Oporowski, Oxley, and Vertigan proved that, for alln⩾3, there is an integerN(n) such t...
AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k...
We refine a property of $2$-connected graphs described in the classical paper of Dirac from 1952 and...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
AbstractDirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected gra...
AbstractWe give a lower bound on the number of edges meeting some vertex of degree k in terms of the...
In this paper we derive several results for connected matroids and use these to obtain new results f...
By a well-known result of Tutte, if e is an element of a connected matroid M, then either the deleti...
Let G be a (multi)graph of order n and let u, v be vertices of G. The maximum number of internally ...
Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say tha...
AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either th...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractThe structure of connected graphs of given size and order that have minimal algebraic connec...
Halin proved that every minimally $k$-connected graph has a vertex of degree $k$. More generally, do...
The edge-connectivity l of a connected graph is the minimum number of edges whose deletion produc...
AbstractDing, Oporowski, Oxley, and Vertigan proved that, for alln⩾3, there is an integerN(n) such t...
AbstractA matroid M is minimally k-connected if M is k-connected and, for every e∈E(M), M\e is not k...
We refine a property of $2$-connected graphs described in the classical paper of Dirac from 1952 and...