The class of graphs with no K3,t-minors, t ≥ 3, contains all planar graphs and plays an important role in graph minor theory. In 1992, Seymour and Thomas conjectured the existence of a function α(t) > 0 and a constant β > 0, such that every 3-connected n-vertex graph with no K3,t-minors, t ≥ 3, contains a cycle of length at least α(t)n . The purpose of this paper is to confirm this conjecture w...

This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more eeciently. Also, several results on graph minors are reviewed.

The extragalactic applications of NIR surveys are summarized with a focus on the ability to map the interstellar extinction of our Galaxy. Very preliminary extraction of galaxies on a set of 180 consecutive images is presented, and the results illustrate some of the pitfalls in attempting an homogeneous extraction of galaxies from these wide-angle and shallow surveys.