Extremal critically connected matroids

  title={Extremal critically connected matroids},
  author={Uppaluri S. R. Murty},
  journal={Discret. Math.},
  • U. Murty
  • Published 1 March 1974
  • Mathematics
  • Discret. Math.
On minimally k-connected matroids
On removable series classes in connected matroids
It is proved that a connected matroid M with r(M) ≥ 2 has at least r( M) + 1 removable series classes.
Elements belonging to triads in 3-connected matroids
Some extremal connectivity results for matroids
Some Local Extremal Connectivity Results for Matroids
Tutte proved that if e is an element of a 3-connected matroid M such that neither M\e nor M/e is 3-connected, then e is in a 3-circuit or a 3-cocircuit. In this paper, we prove a broad generalization
On a matroid generalization of graph connectivity
  • J. Oxley
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1981
This paper relates the concept of n-connection for graphs to Tutte's theory of n-connection for matroids (12). In particular, we show how Tutte's definition may be modified to give a matroid concept
Paths in circuit graphs of matroids
On Extremal Connectivity Properties of Unavoidable Matroids
Each of these classes of unavoidable matroids is characterized in terms of an extremal connectivity condition and it is proved that ifMis a 3-connected matroid of at least rank 7 for which every single-element deletion or contraction is 3- connected but no 2-element contraction is, thenMis a spike with its tip deleted.
Hamilton cycles in circuit graphs of matroids


Minimally 2-connected graphs.
Definition 1. A graph is called 2-connected if it contains at least 2 vertices and each pair of vertices belong to some circuit contained in the graph. For graphs with at least 3 vertices this is
On the Abstract Properties of Linear Dependence
Let C1 , C2 ,· · · ,Cm be the columns of a matrix M. Any subset of these columns is either linearly independent or linearly dependent; the subsets thus fall into two classes. These classes are not
On minimal blocks