Abstract" If a theorem about graphs can be expressed in terms of edges and circuits only it
probably exemplifies a more general theorem about matroids." This assertion, made by Tutte …

The circumference of a graph (resp. matroid) is defined to be the size of its largest cycle
(resp. circuit) and the cocircumference is the size of its largest cocycle (resp. cocircuit). We …

Bonds intersecting cycles in a graph Page 1 COMBINATORICA Bolyai Society – Springer-Verlag
0209–9683/105/$6.00 c 2005 János Bolyai Mathematical Society Combinatorica 25 (4) (2005) …

Let G be a loopless 2-connected graph with circumference c and with largest bond of size
c∗. In an earlier paper, the author proved that| E (G)|⩽ 1 2 cc∗. This paper determines all 2 …

Given a graph G, one can define a matroid M=(E, C) on the edges E of G with circuits C
where C is either the cycles of G or the bicycles of G. The former is called the cycle matroid …

Let M be a connected matroid having a ground set E. Lemos and Oxley proved that| E (M)|≤
12c (M) c∗(M) where c (M)(resp. c∗(M)) is the circumference (resp. cocircumference) of M. In …

The goal of these talks is to give you a good idea of what the field of extremal matroid theory
is about. We will prove some basic results in extremal matroid theory, we will discuss a …

A cycle in a graph is called a hamilton cycle if it passes all vertices of the graph. A problem of
determining whether a given graph has a hamilton cycle or not is important in Graph Theory …

Lovász, Schrijver, and Seymour have shown that if a connected matroid M has a largest
circuit of size c and a largest cocircuit of size c*, then M has at most [special characters …