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Given n subspaces of a finite-dimensional vector space over a fixed finite field F, we wish to find a linear layout V1, V2,. .. , Vn of the subspaces such that dim((V1 +V2 +· · ·+Vi)∩(Vi+1 +· · ·+Vn)) ≤ k for all i; such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the(More)
Reported herein is the metal-catalyzed regioselective C-H functionalization of quinoline N-oxides at the 8-position: direct iodination and amidation were developed using rhodium and iridium catalytic systems, respectively. Mechanistic study of the amidation revealed that the unique regioselectivity is achieved through the smooth formation of(More)
Linear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite obstruction set O k of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in O k. However, no attempts(More)
We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A, B, C ⊆ X with A∪B ∪C = X and |A|, |B|, |C| ≤ k such that any subset of X that is a minimal separator of H is a subset of either A, B or C. Treewidth and branchwidth(More)
Three novel BODIPY-based heterodinuclear complexes, [salen(3,5-(t)Bu)2Al-(OC6H4-BODIPY)] (6), [salen(3,5-(t)Bu)2Al-(OC6F2H2-BODIPY)] (7), and [(mq)2Al-(OC6H4-BODIPY)] (8) (salen = N,N'-bis(salicylidene)ethylenediamine, BODIPY = 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene, and mq = methyl-8-quinolinolato) were prepared and characterized by multinuclear NMR(More)
A change in reaction pathway was achieved for the first time by tuning the cyclopentadienyl (Cp) ligand used for the rhodium-catalyzed cyclization of benzamides with conjugated enynones. Depending on the Cp ligand, the reaction pathway switched between [4+2] and [4+1] annulation. Electronic effects turned out to be crucial for the product distribution. The(More)
The Rh(III)-catalyzed C-8 selective direct alkylation and alkynylation of quinoline N-oxides has been developed. The reactions proceeded highly efficiently at room temperature over a broad range of substrates with excellent regioselectivity and functional group tolerance. This development demonstrates the synthetic utility of the N-oxide directing group as(More)
Deoxygenation of various types of N-oxides including both heterocyclic and alkyl(aryl)amine derivatives has successfully been developed by the copper-catalyzed oxygen atom transfer using diazo compounds as the oxygen acceptor. The reaction proceeds smoothly over a broad range of substrates with excellent functional group tolerance under mild conditions.
A homogeneous set of a graph G is a set X of vertices such that 2 ≤ |X| < |V (G)| and no vertex in V (G) − X has both a neighbor and a non-neighbor in X. A graph is prime if it has no homogeneous set. We present an algorithm to decide whether a class of graphs given by a finite set of forbidden induced subgraphs contains infinitely many non-isomorphic prime(More)