Add to ORKGMader proved that every 2-connected simple graph G with minimum degree d exceeding three has a cycle C, the deletion of whose edges leaves a 2-connected graph. Jackson extended this by showing that C may be chosen to avoid any nominated edge of G and to have length at least d-1. This article proves an extension of Jackson\u27s theorem. In addition, a conjecture of Goddyn, van den Heuvel, and McGuinness is disproved when it is shown that a natural matroid dual of Mader\u27s theorem fails. © 1999 John Wiley & Sons, Inc
We prove there exists a function f (k) such that for every f (k)-connected graph G and for every edg...
Las Vergnas & Hamidoune studied the number of circuits needed to deter-mine an oriented matroid....
An essential element of a 3-connected matroid M is one for which neither the deletion nor the contra...
Mader and Jackson independently proved that every 2-connected simple graph G with minimum degree at ...
We show that if M is a connected binary matroid of cogirth at least five which does not have both an...
AbstractWe prove the following conjecture of Bill Jackson (J. London Math. Soc. (2)21, 1980, 391).If...
For a k-connected graph or matroid M, where k is a fixed positive integer, we say that a subset X of...
In this paper we derive several results for connected matroids and use these to obtain new results f...
AbstractFor a k-connected graph or matroid M, where k is a fixed positive integer, we say that a sub...
AbstractMatroidal families are defined as families of connected graphs such that, given any graph G,...
We verify two special cases of Thomassen’s conjecture of 1976 stating that every longest cycle in a ...
The classical Whitney's 2-Isomorphism Theorem describes the families of graphs having the same cycle...
AbstractIn this paper we prove the following theorem: Let M be a 3-connected matroid other than the ...
Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connecte...
AbstractLet G be a 2-connected undirected graph with n vertices. Its connected subgraphs of n−1 edge...
We prove there exists a function f (k) such that for every f (k)-connected graph G and for every edg...
Las Vergnas & Hamidoune studied the number of circuits needed to deter-mine an oriented matroid....
An essential element of a 3-connected matroid M is one for which neither the deletion nor the contra...
Mader and Jackson independently proved that every 2-connected simple graph G with minimum degree at ...
We show that if M is a connected binary matroid of cogirth at least five which does not have both an...
AbstractWe prove the following conjecture of Bill Jackson (J. London Math. Soc. (2)21, 1980, 391).If...
For a k-connected graph or matroid M, where k is a fixed positive integer, we say that a subset X of...
In this paper we derive several results for connected matroids and use these to obtain new results f...
AbstractFor a k-connected graph or matroid M, where k is a fixed positive integer, we say that a sub...
AbstractMatroidal families are defined as families of connected graphs such that, given any graph G,...
We verify two special cases of Thomassen’s conjecture of 1976 stating that every longest cycle in a ...
The classical Whitney's 2-Isomorphism Theorem describes the families of graphs having the same cycle...
AbstractIn this paper we prove the following theorem: Let M be a 3-connected matroid other than the ...
Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connecte...
AbstractLet G be a 2-connected undirected graph with n vertices. Its connected subgraphs of n−1 edge...
We prove there exists a function f (k) such that for every f (k)-connected graph G and for every edg...
Las Vergnas & Hamidoune studied the number of circuits needed to deter-mine an oriented matroid....
An essential element of a 3-connected matroid M is one for which neither the deletion nor the contra...