We report the 4.682-Mbp high-quality draft assembly of the Escherichia coli strain ATCC 23502 (serovar O5:K4:H4, also known as NCDC U1-41) genome. This uropathogenic strain, commonly referred to as E. coli K4, produces a glycosaminoglycan-like capsular polysaccharide with a backbone similar in structure to unsulfated chondroitin, a precursor to the nutraceutically and potentially pharmaceutical...

The k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K4) of K4 or G is obtained from the wheel Wk (k¿ 3) by subdividing any of its outer-edges with an odd number of vertices. c © 2003 Elsevier B.V. All rights reserved.

Given two 3-uniform hypergraphs F and G = (V,E), we say that G has an F -covering if we can cover V with copies of F . The minimum codegree of G is the largest integer d such that every pair of vertices from V is contained in at least d triples from E. Define c2(n, F ) to be the largest minimum codegree among all n-vertex 3-graphs G that contain no F -covering. Determining c2(n, F ) is a natura...

Many useful classes of graphs can in principle be recognized with finite batteries of obstruction tests. One of the most fundamental tests is to determine whether an arbitrary input graph contains K4 in the immersion order. In this paper, we present for the first time a fast, practical algorithm to accomplish this task. We also extend our method so that, should an immersed K4 be present, a K4 m...

Monosubstituted cycloalkanes undergo regio- and enantioselective aliphatic C-H oxidation with H2O2 catalyzed by biologically inspired manganese catalysts. The reaction furnishes the corresponding ketones resulting from oxidation at C3 and C4 methylenic sites (K3 and K4, respectively) leading to a chiral desymmetrization that proceeds with remarkable enantioselectivity (64% ee) but modest regios...

Gene duplication followed by functional specialization is a potent force in the evolution of biological diversity. A comparative study of two highly conserved duplicated genes, ARABIDOPSIS TRITHORAX-LIKE PROTEIN1 (ATX1) and ATX2, revealed features of both partial redundancy and of functional divergence. Although structurally similar, their regulatory sequences have diverged, resulting in distin...

Fix positive integers p, q, and r so that p is prime, q = p, and q ≡ 1 (mod 4). Fix a graph G as follows: If r is odd or p 6≡ 3 (mod 4), let G be the qvertex Paley graph; if r is even and p ≡ 3 (mod 4), let G be either the q-vertex Paley graph or the q-vertex Peisert graph. We use the subgraph structure of G to construct four sequences of 2-designs, and we compute their parameters. Letting k4 d...

A method of construction of C-ultrahomogeneous (or C-UH) graphs is applied to the Biggs-Smith graph, which is seen in the process to be a {C9}P4 -UH graph and a { ~ C9} ~ P4 -UH digraph, in order to demonstrate the existence of a connected edge-disjoint union Y of 102 tetrahedra (K4 s), or also union Y of 102 cuboctahedra (L(Q3) s) with no common 4-cycles, possesing a C-UH property for C = {K4}...

Hugo Hadwiger proved that a graph that is not 3-colorable must have a K4minor and conjectured that a graph that is not k-colorable must have a Kk+1minor. By using the Hochstättler-Nešetřil definition for the chromatic number of an oriented matroid, we formulate a generalized version of Hadwiger’s conjecture that might hold for the class of oriented matroids. In particular, it is possible that e...