Stephan Brandt

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Let S(H) be the minimum degree of the graph H. We prove that a graph H of order n with S(H) ^ (2n —1)/3 contains any graph G of order at most n and maximum degree A(G) < 2 as a subgraph, and this bound is best possible. Furthermore, this result settles the case A(G) = 2 of the well-known conjecture of Bollobas, Catlin and Eldridge on packing two graphs with(More)
Plant organs are composed of many different cell types and the analysis of 'bulk' material results in the average of all information in these cells. Therefore, this does not reflect any individuality of the tissues present in plants. This review briefly summarizes different sampling methods which provide tissue- and cell-specific samples, respectively. In(More)
In generalizing the concept of a pancyclic graph, we say that a graph is ‘weakly pancyclic’ if it contains cycles of every length between the length of a shortest and a longest cycle. In this paper it is shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic are considerably weaker than those required to ensure that it(More)
In the class of k-connected claw-free graphs, we study the stability of some hamilto-nian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an innnite family of graphs G k of(More)
Advances in high-throughput genome sequencing demand the development of more efficient ways of examining gene expression at a cellular level. During recent years, polymerase chain reaction (PCR)-based methods have been developed that allow the amplification of mRNA from small amounts of material, even from single animal cells. In parallel, several(More)
Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f(k) vertices whenever k ≤ (n− f(k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is linear). We show that an f -connected graph contains a cycle of length linear in n if f is(More)