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Search results for: CHROMATIC SUM
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Total chromatic sum for trees
PublicationThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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Edge-chromatic sum of trees and bounded cyclicity graphs
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublicationWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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Reactions of R<sub>2</sub>P-P(SiMe<sub>3</sub>)Li with [(R'<sub>3</sub>P)<sub>2</sub>PtCl<sub>2</sub>]. A General and Efficient Entrance to Phosphanylphosphinidene Complexes of Platinum. Syntheses and Structures of [(η<sub>2</sub>-P=P<sup>i</sup>Pr<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [(η<sub>2</sub>-P=P<sup>t</sup>Bu<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [{η<sub>2</sub>-P=P(N<sup>i</sup>Pr<sub>2</sub>)2}Pt(p-Tol<sub>3</sub>P)<sub>2</sub>] and [{(Et<sub>2</sub>PhP)<sub>2</sub>Pt}<sub>2</sub>P<sub>2</sub>].
PublicationReakcje pochodnych litowych difosfanów R2P-P(SiMe3)Li z (R'3P)2PtCl2 zachodzą łatwo i prowadzą do wytworzenia bocznie (side-on) związanych fosfanofosfinidenowych kompleksów platyny [(η2-P=PR2)Pt(PR'3)2] (dla R=tBu, iPr, Et2N, iPr2N). Reakcja Ph2P-P(SiMe3)Li...
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Synthesis, structure characterization and thermal propertiesof [Zr<sub>6</sub>(μ<sub>3</sub>-O)<sub>4</sub>(μ<sub>3</sub>-OH)<sub>4</sub>(OOCCH<sub>2</sub><sup>t</sup>Bu)<sub>9</sub>(μ<sub>2</sub>-OH)<sub>3</sub>]<sub>2</sub>
PublicationTytułowy związek otrzymano w reakcji Zr(OiPr)4 z nadmiarem kwasu 3,3-dimetylobutyrowego. Rentgenowska analiza strukturalna została wykonana w temperaturze 103 i 153K. Struktury zawierają dimery podjednostek o wzorze: [Zr6(μ3-O)4(μ3-OH)4-(OOCCH2tBu)9] połączonych 6 mostkującymi grupami μ2-OH. Analiza zmiennotemperaturowych...
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Epigenetics & Chromatin
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Sum Coloring of Graphs.
PublicationRozdział jest poświęcony sumacyjnemu kolorowaniu grafów. Przedstawiono jego podstawowe własności oraz zastosowania praktyczne.
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The crystal structures of (<i>O</i>-silyl)thiobenzoates (<sup><i>t</i></sup>BuO)<sub>3</sub>SiOC(S)Ph, Ph<sub>3</sub>SiOC(S)Ph, (2,6-XyO)<sub>3</sub>SiOC(S)Ph, and PhC(O)SSSC(O)Ph
PublicationChlorek benzylu reaguje z silanotiolanami sodu R3SiSNa dając wyłącznie pochodne sililowe kwasu monotiobenzoesowego R3SiOC(S)Ph, R=t-Bu, Ph lub 2,6-XyO w postaci pomarańczowych kryształów. Wymienione produkty zostały poddane rentgenowskiej analizie strukturalnej. Badania NMR roztworów tych substancji wskazują, że te same izomery są obecne w roztworze i w ciele stałym.
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Infinite chromatic games
PublicationIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Shape resonance of H[sub 2][sup −] anion stabilized in a molecular trap
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