A Linear Algorithm for Finding Total Colorings of Partial k-Trees

Isobe, Shuji; Zhou, Xiao; Nishizeki, Takao

doi:10.1007/3-540-46632-0_35

Cited by 4 publications

(7 citation statements)

References 10 publications

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“…However, in [2 + 2] and [4 + 2] cycloaddition reactions, one of the dimers remains asymmetric with a tilt angle and this empty dimer may lead to a higher energy due to the unsaturated electronic configuration. This result is consistent with refs[56] and[57], in which the bridge-type adsorption of thiophene (a 5-membered aromatic ring with the formula of C 4 H 4 S) and benzene (a 6-membered aromatic ring with the formula of C 6 H 6 ) on Si(001) was found to be more stable than [4+2] cycloaddition, respectively.…”

supporting

confidence: 92%

Functionalization of silicon surface by thiadiazole molecule: A DFT study

Kaderoğlu

2018

Surface Science

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The first principles density functional theory (DFT) calculations have been used to investigate the atomic and electronic properties of thiadiazole adsorption on the Si (001) surface. A (2×2) reconstructed clean substrate surface has been chosen to give the molecule sufficient space to relax into its most favorable position. A total of eighteen bonding model including bridge-type bonding, and [2+2]/[4+2] cycloaddition mechanisms for four structural isomers of thiadiazole molecule have been discussed in these calculations. The most stable bonding configuration for each of the four isomers on the clean silicon surface has been determined by performing total energy calculations.Electronic structures of the stable surfaces have been investigated by plotting the total density of states (TDOS) and energy band diagrams. Charge densities have been plotted to determine the origin of the surface states appeared in the fundamental band gap of silicon. Finally, partial density of states (PDOS) have been plotted to see the contributions from s-and p-orbitals.

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confidence: 92%

Functionalization of silicon surface by thiadiazole molecule: A DFT study

Kaderoğlu

2018

Surface Science

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“…Recently, we studied η 5oxopentadienyl ruthenium complexes that were found to undergo oxidative addition of SnCl 4 , I 2 , and O 2 , yielding Cp*Ru (IV) (η 3 -oxopentadienyl)(X 1 )(X 2 ) derivatives readily. 1 Maitlis and co-workers demonstrated the accessibility of pentamethylcyclopentadienyl-substituted organoiridium(V) 42 and organorhodium(V) 43 complexes. Other examples reported in the literature are Cp*IrH 4 44 and Cp*Ir(η 2 -2,5-Me 2 -thiophene)(H) 2 .…”

Section: Resultsmentioning

confidence: 99%

“…Found: C, 36.47; H, 4.68. MS: 467(4) [M -PF6 + ], 425 (42), 313 (40). IR (CHCl3, cm -1 ): 1677 (CdO).…”

Section: Synthesis Of Cp*rhcl[η 3 -Ch2c(me)chc(me)o] (10)mentioning

confidence: 99%

Synthesis, Structure, Spectroscopy, and Reactivity of Half-Open Rhodocenium and Iridocenium with Oxodienyl Ligands

2002

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The syntheses of the oxopentadienyl complex [Cp*Rh(η5-CH2C(Me)CHC(Me)O)][BF4] (6) and the iridaoxabenzene [Cp*IrAg2(μ2-OPF2O)2(1,5-η-CHC(CMe3)CHC(CMe3)O)] (9) are reported. Compound 9 is an organometallic polymer, formed in competition with complex [(Cp*Ir)2(μ2-OPF2O)3][PF6] (8). Treatment of [Cp*MCl2]2 (M = Rh, Ir) with lithium 2-methyl-4-oxopentadienide produces Cp*M(Cl)[η3-CH2C(Me)CHC(Me)(O)] (M = Ir, 7; Rh, 10). 1H and 13C NMR, as well as IR spectra, indicate that the ligand acts as an η3-oxodienyl group with an exo-syn conformation. The addition of phosphines, PR3 (R = Ph, Me or PR3 = PHPh2), in acetone to compound [Cp*Ir(η5-CH2C(Me)CHC(Me)O)][PF6] (1) led to the formation of isomers [Cp*Ir(1,5-η-CH2C(Me)CHC(Me)O)(L)][PF6] [L = PMe3, 11; PPh3, 15] and [Cp*Ir(η3-CH2C(Me)CHC(Me)O)(L)][PF6] [L = PMe3, 12; PHPh2, 14; PPh3, 16]. The 1,5-η and the η3 isomers are the kinetic and thermodynamic products, respectively. The addition of phosphines PR3 (R = Me, Ph) in methylene chloride to compound 6 led to the formation of compounds [Cp*Rh(η3-CH2C(Me)CHC(Me)O)(L)][BF4] [L = PMe3, 18; PPh3, 20]. Compounds 18, 20, and [Cp*Rh(η3-CH2C(Me)CHC(Me)O)(PHPh2)][OTf] (21) can also be obtained by adding the corresponding phosphine to compound 10, followed by the addition of AgOTf. The addition at room temperature of acetonitrile to compound 1 led to the formation of [Cp*Ir(η3-CH2C(Me)CHC(Me)O)(NCMe)][PF6] (22), with an exo-anti conformation of the oxodienyl ligand. Facile dissociation of MeCN became evident. The exo-anti isomer structure of 22 has unequivocally been established by an X-ray diffraction study. The analogous rhodium exo-syn isomer [Cp*Rh(η3-CH2C(Me)CHC(Me)O)(NCMe)][BF4] (23) has been established by 1H and 13C NMR spectroscopy. Exo-anti and exo-syn preferences have been established for all synthesized rhodium and iridium compounds. Compounds 1 and 6 did not suffer oxidative addition with SnCl4 and I2. With I2 the bridged iodine compounds [(Cp*M)2(μ2-I)3][X] (M = Ir, X = PF6, 25; M = Rh, X = BF4, 26) were obtained. Crystal structures for iridium compounds 1, 9, 22, and 25 and rhodium compounds 6, 10, 18, and [Cp*Rh(η3-CH2C(Me)CHC(Me)O)(H2O)][BF4] (24) are described.

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“…[4]. In an earlier version [9] of this paper, we showed that χ t (G)= ∆(G)+1 if G is s-degenerate and ∆(G) ≥ 4s 2 . Theorem 3.1 is better than these results.…”

Section: Main Theoremmentioning

confidence: 86%

“…Hence the total coloring problem can be solved in time O(n log n) for a fairly large class of graphs including all planar graphs with sufficiently large maximum degree. We finally show that the total coloring problem can be solved in linear time for partial k-trees G with bounded k. Earlier versions of this paper were presented at [9,10].…”

Section: Introductionmentioning

confidence: 91%

Total Colorings Of Degenerate Graphs

2007

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A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is sdegenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerate graph G has a total coloring with ∆+1 colors if the maximum degree ∆ of G is sufficiently large, say ∆ ≥ 4s+3. Our proof yields an efficient algorithm to find such a total coloring. We also give a lineartime algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, that is, the tree-width of G is bounded by a fixed integer k.

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A Linear Algorithm for Finding Total Colorings of Partial k-Trees

Cited by 4 publications

References 10 publications

Functionalization of silicon surface by thiadiazole molecule: A DFT study

Functionalization of silicon surface by thiadiazole molecule: A DFT study

Synthesis, Structure, Spectroscopy, and Reactivity of Half-Open Rhodocenium and Iridocenium with Oxodienyl Ligands

Total Colorings Of Degenerate Graphs

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