๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Basis pair graphs of transversal matroids are connected

โœ Scribed by Martin Farber

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
460 KB
Volume
73
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

The basis pair graph of a matroid on the ground set S has, as its vertices, ordered triples of the form (&, &, &), where B, and B2 are disjoint bases and B3 = S(B, U 4). Two such vertices, (AI, AZ, As) and (Ri, B,, IQ, are adjacent if (B,, &, B3) can be obtained from (AI, A*, As) by interchanging two elements of S belonging to different component, of (Al, At, As). It is known that basis pair graphs of grap%-1 cI zx! cographic matroids are connected. We show that this holds for transversal matroids as well.

๐Ÿ“œ SIMILAR VOLUMES

On the Structure of 3-connected Matroids
On the Structure of 3-connected Matroids and Graphs
โœ James Oxley; Haidong Wu ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 249 KB

An element e of a 3-connected matroid M is essential if neither the deletion M\e nor the contraction M/e is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In this paper, we consider those 3-conne

Matroidal families of finite connected n
Matroidal families of finite connected nonhomeomorphic graphs exist
โœ Thomas Andreae ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 197 KB

## Abstract A matroidal family is a nonempty set โ„ฑ of connected finite graphs such that for every arbitrary finite graph __G__ the edge sets of the subgraphs of __G__ which are isomorphic to an element of โ„ฑ form a matroid on the edge set of __G__. In the present paper the question whether there are

All 4-connected Line Graphs of Claw Free
All 4-connected Line Graphs of Claw Free Graphs Are Hamiltonian Connected
โœ Matthias Kriesell ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 109 KB

Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.

A lower bound on connectivities of matro
A lower bound on connectivities of matroid base graphs
โœ Guizhen Liu ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 853 KB

The connectivity of a graph G and the corank of a matroid M are denoted by K(G) and p, respectively. X is shown that if a graph G is the base graph of a simple mat&d M, then K(G) L 2p and the lower bound of 2p izA best possible.