For all positive integers k, the class Bk of matroids of branch-width at most k is minor-closed. When k is 1 or 2, the class Bk is, respectively, the class of direct sums of loops and coloops, and the class of direct sums of seriesparallel networks. B3 is a much richer class as it contains infinite antichains of matroids and is thus not well-quasi-ordered under the minor order. In this paper, i...

The interaction of DNA with proteins occurs over a wide range of length scales, and depends critically on its local structure. In particular, recent experimental work suggests that the intrinsic curvature of DNA plays a significant role on its protein-binding properties. In this work, we present a coarse grained model of DNA that is capable of describing base-pairing, hybridization, major and m...

This paper considers the following question: What is the maximum number of k-cliques in an n-vertex graph with no Kt-minor? This question generalises the extremal function for Kt-minors, which corresponds to the k = 2 case. The exact answer is given for t 6 9 and all values of k. We also determine the maximum total number of cliques in an n-vertex graph with no Kt-minor for t 6 9. Several obser...

It is well known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalize the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large mi...

Since 1955 at least forty articles on geriatric anaesthesia and associated problems have appeared in the literature. Fifteen of these have been written in English and the others in European languages, mostly German and Italian. Fourteen of the fifteen English articles have originated from North America. To the best of the writer's knowledge this leaves Bedford's (1955) contribution as one of th...