Coloring planar graphs in parallel

We present NC algorithms for vertex and edge coloring planar graphs. The vertex coloring algorithm 5 colors any planar graph, and the edge coloring algorithm Δ edge colors planar graphs with Δ ≥ 23 (and Δ + 1 edge colors planar graphs with Δ < 23), where Δ is the maximum degree in the graph.     

Studying links via closed braids IV: composite links and split links

Summary The main result concerns changing an arbitrary closed braid representative of a split or composite link to one which is obviously recognizable as being split or composite. Exchange moves are introduced; they change the conjugacy class of a closed braid without changing its link type or its braid index. A closed braid representative of a composite (respectively split) link is composite (split) if there is a 2-sphere which realizes the connected sum decomposition (splitting) and meets the braid axis in 2 points. It is proved that exchange moves are the only obstruction to representing composite or split links by composite or split closed braids. A special version of these theorems holds for 3 and 4 braids, answering a question of H. Morton. As an immediate Corollary, it follows that braid index is additive (resp. additive minus 1) under disjoint union (resp. connected sum).Oblatum 29-XI-1988 & 25-I-1990Partially supported by NSF Grant #DMS-88-05672     

On list‐coloring outerplanar graphs

We prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) with a list of colors L (v ) for each vertex v such that (resp., ) can be L‐list‐colored (except when the graph is K₃ with identical 2‐lists). These results are best possible for each condition in the hypotheses and bounds. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 59–74, 2008     

Characterisation and cryomagnetic study of a hydrothermally synthesised hydrogen bonded L–M–L type co-ordination polymer

A ligand–metal–ligand type co-ordination polymer [Ni (C₆H₁₂N₄)(NCS)₂(H₂O)₂] _n has been synthesised under controlled hydrothermal conditions. Here 1,3,5,7-tetraazatricyclo[3.3.1]decane [or hexamethylenetetramine (hmt)] has been used as a μ-(N,N′) bidentate spacer molecule. The prepared polymeric complex has been characterised by elemental and spectral analyses. The structure has been confirmed by a single crystal X-ray diffraction study. Magneto-structural correlation has been drawn from cryomagnetic susceptibility measurements (2–300 K) which unequivocally reflects very weak magnetic spin interactions among the long distant octahedral Ni(II) metal centres mediated by hmt and weak hydrogen bonding interactions between the adjacent zigzag one-dimensional polymeric chains carrying into a two-dimensional infinite polymeric framework.     

Synthesis,Characterisation, and in vitro Cytotoxic Activity of Dithiocarbamato Glycoconjugate Half-Sandwich Ruthenium and Osmium Complexes

The synthesis by transmetallation and in-depth characterisation by IR spectroscopy of five half-sandwich ruthenium and osmium dithiocarbamato isonipecotamide glycoconjugate complexes are presented herein. The evaluation of their in vitro cytotoxicity and of the zinc precursors’ in vitro cytotoxicity towards ovarian cancer (A2780 and A2780cisR) and normal prostate (PNT2) cells is reported. While the cytotoxicity of the compounds is rather limited, some selectivity is observed.     

Synthesis, crystal structure, and magnetic studies of one-dimensional cyano-bridged Ln3+-Cr3+ complexes with bpy as a blocking ligand

The reaction of Ln(NO3)3.aq with K3[Cr(CN)6] and 2,2'-bipyridine (bpy) in a water/ethanol solution led to two families of complexes: 4 one-dimensional (1D) complexes of the formula trans-[Cr(CN)4(mu-CN)2Ln(H2O)3(bpy)2]n.4nH2O.3.5nbpy (Ln3+ = La, Ce, Pr, and Nd) and 10 1D complexes of the formula trans-[Cr(CN)4(mu-CN)2Ln(H2O)4(bpy)]n.3.5nH2O.1.5nbpy (Ln3+ = Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, and Lu). The structures for the fourteen complexes [LaCr]n (1), [CeCr]n (2), [PrCr]n (3), [NdCr]n (4), [NdCr]n (4'), [SmCr]n (5), [EuCr]n (6), [TbCr]n (7), [DyCr]n (8), [HoCr]n (9), [ErCr]n (10), [TmCr]n (11), [YbCr]n (12), and [LuCr]n (13) have been solved. Complexes 1-4 crystallize in the orthorhombic space group Pbam and are isomorphous; complexes 4'-13 crystallize in the triclinic space group PI and are isomorphous. The X-ray structural characterization of complexes 1-4 shows the presence of a discrete decameric water cluster built around a cyclic hexameric core stabilized by the solid-state structure, which represents another new mode of association of water molecules. The Ln3+-Cr3+ magnetic interaction is negligible in 6 and 12, antiferromagnetic in 2, 4', 7, 8, 9, 10, and 11, and unresolved for 3. The complex 5 is a ferrimagnet because its magnetic studies suggest the onset of a very weak ferromagnetic three-dimensional ordering.     

Innovative beneficial reuse of reverse osmosis concentrate using bipolar membrane electrodialysis and electrochlorination processes

Reverse osmosis (RO) is a widely used and rapidly growing desalination technology. A major disadvantage of this process is that the concentrate from the RO process, which could be as much as 25% of the feed stream, represents a polluting stream. This waste stream could pose a significant challenge to the implementation of this process, particularly for inland communities which do not have the option of ocean disposal. An excellent environmentally benign approach to disposal could be beneficial reuse of the waste stream. This study presents two innovative beneficial reuse strategies for RO concentrate produced by an integrated membrane system (IMS) from a wastewater reclamation facility. The technologies evaluated in this study included bipolar membrane electrodialysis (BMED) for conversion of RO concentrate into mixed acid and mixed base streams, and electrochlorination (EC) for onsite chlorine generation. Bench-scale studies conducted with BMED demonstrated that RO concentrate could be desalted while producing mixed acids and mixed bases with concentrations as high as 0.2N. Similarly, the EC process was capable of producing a 0.6% hypochlorite solution from RO concentrate. The acids and bases as well as the hypochlorite produced could be directly applied to the RO process as well as upstream pre-treatment processes. A preliminary economic evaluation of the viability of these two approaches was conducted by conducting rough order of magnitude cost estimates based on the bench-scale performance of these processes on RO concentrate. A comparison of the overall costs of an Integrated Membrane System utilizing these innovative reuse strategies with conventional disposal options and thermal zero liquid discharge treatment is presented. This comparison indicates that a reuse approach might be economically viable for inland wastewater reuse facilities that utilize RO membranes and have limited options for concentrate disposal.     

Structural diversity in manganese squarate frameworks using N,N-donor chelating/bridging ligands: syntheses, crystal structures and magnetic properties

Three new polymeric squarato-bridged manganese complexes {[Mn(H(2)O)(2)(bpe)(sq)].bpe.H(2)O}(n) (1), [Mn(2)(H(2)O)(4)(phen)(2)(sq)(2)](n) (2) and [Mn(2)(H(2)O)(2)(phen)(4)(sq)].(sq).8(H(2)O) (3) [bpe, 1,2-bis(4-pyridyl)ethane; phen, 1,10-phenanthroline; sq, squarate dianion] have been synthesized and characterized by single crystal X-ray diffraction analysis and variable temperature magnetic studies. Complex 1 is a 2D rectangular grid-like structure, achieved through flexible bpe bridging ligands and squarate dianions. On the other hand the use of chelating phen instead of bpe gives rise to a 1D polymeric chain in complex 2 and to a dinuclear entity in 3. In all the three complexes weak interactions play a vital role in stabilizing the solid-state structure. Variable temperature (2-300 K) magnetic studies indicate weak antiferromagnetic coupling between the metal centres in all the complexes.     

Molecular-programmed self-assembly of homo- and heterometallic penta- and hexanuclear coordination compounds: synthesis, crystal structures, and magnetic properties of ladder-type CuII2MIIx (M=Cu, Ni; x=3, 4) oxamato complexes with CuII2 metallacyclophane cores

New homo- and heterometallic, hexa- and pentanuclear complexes of formula {[Cu2(mpba)2(H2O)F][Cu(Me5dien)]4}(PF6)(3).5H2O (1), {[Cu2(Me3mpba)2(H2O)2][Cu(Me5dien)]4}(ClO4)(4).12H2O (2), {[Cu2(ppba)2][Cu(Me5dien)]4}(ClO4)4 (3), and [Ni(cyclam)]{[Cu2(mpba)2][Ni(cyclam)]3}(ClO4)(4).6H2O (4) [mpba=1,3-phenylenebis(oxamate), Me3mpba=2,4,6-trimethyl-1,3-phenylenebis(oxamate), ppba=1,4-phenylenebis(oxamate), Me5dien=N,N,N'N' ',N' '-pentamethyldiethylenetriamine, and cyclam=1,4,8,11-tetraazacyclotetradecane] have been synthesized through the use of the "complex-as-ligand/complex-as-metal" strategy. The structures of 1-3 consist of cationic CuII6 entities with an overall [2x2] ladder-type architecture which is made up of two oxamato-bridged CuII3 linear units connected through two m- or p-phenylenediamidate bridges between the two central copper atoms to give a binuclear metallacyclic core of the cyclophane-type. Complex 4 consists of cationic CuII2NiII3 entities with an incomplete [2x2] ladder-type architecture which is made up of oxamato-bridged CuIINiII and CuIINiII2 linear units connected through two m-phenylenediamidate bridges between the two copper atoms to give a binuclear metallacyclophane core. The magnetic properties of 1-3 and 4 have been interpreted according to their distinct "dimer-of-trimers" and "dimer-plus-trimer" structures, respectively, (H=-J(S1A.S3A+S1A.S4A+S2B.S5B+S2B.S6B)-J'S1A.S2B). Complexes 1-4 exhibit moderate to strong antiferromagnetic coupling through the oxamate bridges (-JCu-Cu=81.3-105.9 cm-1; -JCu-Ni=111.6 cm-1) in the trinuclear and/or binuclear units. Within the binuclear metallacyclophane core, a weak to moderate ferromagnetic coupling (J'Cu-Cu=1.7-9.0 cm-1) operates through the double m-phenylenediamidate bridge, while a strong antiferromagnetic coupling (J'Cu-Cu=-120.6 cm-1) is mediated by the double p-phenylenediamidate bridge.