We announce the availability of the 5.023-Mbp high-quality draft assembly of the Escherichia coli strain Nissle 1917 (serovar O6:K5:H1) genome. Short genomic segments from this important probiotic strain have been available in public databases, but the full genome sequence has remained inaccessible. Thus, high-coverage, whole genome sequencing of E. coli Nissle 1917 is presented herein. Reannot...

For any collection of graphs G1, . . . , GN we find the minimal dimension d such that the product G1 × · · · ×GN is embeddable into R . In particular, we prove that (K5) and (K3,3) are not embeddable into R, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we s...

We prove that a binary geometry of rank n {n > 2) not containing M(Ky and F-, (respectively, M(K5) and C10) as a minor has at most 3/i 3 (respectively, 4« 5) points. Here, M(K5) is the cycle geometry of the complete graph on five vertices, F-, the Fano plane, and C10 a certain rank 4 ten-point geometry containing the dual Fano plane F* as a minor. Our technique is elementary and uses the notion...

We determine the value of the Ramsey number R(W5, K5) to be 27, where W5 = K1 + C4 is the 4-spoked wheel of order 5. This solves one of the four remaining open cases in the tables given in 1989 by George R. T. Hendry, which included the Ramsey numbers R(G, H) for all pairs of graphs G and H having five vertices, except seven entries. In addition, we show that there exists a unique up to isomorp...

where k, is the rate constant for the electron transfer process, K1 the equiiibrium constant for dissociation of [Cr(Lh(H20h+l to [Cr(Lh(H20)(0H)] + W, and K5 the pre-equilibrium format ion constant. Values of k2 = 2.93xl0s• K1 = 6.26 x 10--4 mol dmand K5 = 88.4 1 dm mor 1 have been obtained at 30°C and I= 0.2 mol dmThermodynamic activation parameters have been calculated. It is proposed that e...

Erratum for Mirhendi et al., the first case of onychomycosis in a koala (phascolarctos cinereus) due to atypical isolates of Microsporum gypseum, a diagnostic challenge Mirhendi H1,2*, Nishiyama Y3, Rezaei-Matehkolaei A4, Satoh K5, Makimura K5 1. Department of Medical Parasitology & Mycology, School of Medicine, Isfahan University of Medical Sciences, Isfahan, Iran 2. Department of Medi...

Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove this conjecture for graphs containing K− 4 . AMS Subject Classification: 05C

Let G be an eulerian graph. For each vertex v # V(G), let P(v) be a partition of the edges incident with v and set P= v # V(G) P(v), called a forbidden system of G. We say that P is admissible if |P & T | 2 |T | for every P # P and every edge cut T of G. H. Fleischner and A. Frank (1990, J. Combin. Theory Ser. B 50, 245 253) proved that if G is planar and P is any admissible forbidden system of...

There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with “small” graphs. Let H be the 5-vertex graph defined from K5 by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H ×Pn and H ×Cn, showing that in the general case the corresponding crossing numbers are 3n−1...

Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals Bn(s) := 〈|~r|〉; ~r ∈ [0, 1]. In particular we resolve an elusive integral called K5 that previously acted as a blockade against closed-form evaluation in n = 5 dimensions. In consequence we now know that Bn(integer) can be given a closed form for n = 1, 2, 3,...