Decomposition of regular matroids

It is proved that every regular matroid may be constructed by piecing together graphic and cographic matroids and copies of a certain 10-element matroid.     

Synthesis and reactivity of a conveniently prepared two-coordinate bis(amido) nickel(II) complex

A strictly two-coordinate nickel(II) bis(amido) complex has been prepared and its reactivity towards a variety of small molecules is described. Ni[N(SiMe(3))(DIPP)](2) reacts with DMAP and acetonitrile to form T-shaped three-coordinate complexes, and preliminary results show that Ni[N(SiMe(3))(DIPP)](2) is a catalyst for the hydrosilation of olefins with secondary silanes at ambient temperature.     

A novel structural form of MIL-53 observed for the scandium analogue and its response to temperature variation and CO2 adsorption

The scandium analogue of the flexible terephthalate MIL-53 yields a novel closed pore structure upon removal of guest molecules which has unusual thermal behaviour and stepwise opening during CO(2) adsorption. By contrast, the nitro-functionalised MIL-53(Sc) cannot fully close and the structure possesses permanent porosity for CO(2).     

Tournament immersion and cutwidth

A (loopless) digraph H is strongly immersed in a digraph G if the vertices of H are mapped to distinct vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths used are pairwise edge-disjoint, and do not pass through vertices of G that are images of vertices of H. A digraph has cutwidth at most k if its vertices can be ordered {v₁,…,vn} in such a way that for each j, there are at most k edges uv such that u∈{v₁,…,vj−1} and v∈{vj,…,vn}.We prove that for every set S of tournaments, the following are equivalent:

•

there is a digraph H such that H cannot be strongly immersed in any member of S,

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there exists k such that every member of S has cutwidth at most k,

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there exists k such that every vertex of every member of S belongs to at most k edge-disjoint directed cycles.

This is a key lemma towards two results that will be presented in later papers: first, that strong immersion is a well-quasi-order for tournaments, and second, that there is a polynomial time algorithm for the k edge-disjoint directed paths problem (for fixed k) in a tournament.     

Triangle-free graphs with no six-vertex induced path

The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are three examples: the 16-vertex Clebsch graph, the graph obtained from an 8-cycle by making opposite vertices adjacent, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected triangle-free graph with no six-vertex induced path is an induced subgraph of one of these three (modulo some twinning and duplication).     

Chiral recognition in solution and the gas phase. Experimental and theoretical studies of aromatic D- and L-amino acid–Cu(II)–chiragen complexes Jennifer L. Seymour František Tureček Andrei V. Malkov Pavel Kočovský Journal of Mass Spectrometry 2004; 39: 1044–1052

The original article to which this Erratum refers was published in Journal of Mass Spectrometry 2004; 39: 1044–1052.