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acyclic 6-choosability of planar graphs without adjacent short cycles

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Science China Mathematics 2014年第1期57卷 197-209页

作者： WANG WeiFan ZHANG Ge CHEN Min Department of Mathematics Zhejiang Normal University

A proper vertex coloring of a graph G is acyclic if G contains no bicolored *** a list assignment L={L(v)|v∈V}of G,we say that G is acyclically L-colorable if there exists a proper acyclic coloringπof G such thatπ(v)∈L(v)for all v∈*** G is acyclically L-colorable for any list assignment L with|L(v)|k for all v∈V(G),then G is acyclically *** this paper,we prove that every planar graph G is acyclically 6-choosable if G does not contain 4-cycles adjacent to i-cycles for each i∈{3,4,5,6}.This improves the result by Wang and Chen(2009).

关键词： acyclic coloring,acyclic choosability,planar graph

acyclic edge colorings of planar graphs and series-parallel graphs

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Science China Mathematics 2009年第3期52卷 605-616页

作者： HOU JianFeng WU JianLiang LIU GuiZhen LIU Bin Department of Mathematics Shandong UniversityJinan 250100China

A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that a (G) Δ(G) + 2 for any graphs. For planar graphs G with girth g(G), we prove that a (G) max{2Δ(G) + 2, Δ(G) + 22} if g(G) 3, a (G) Δ(G) + 2 if g(G) 5, a (G) Δ(G) + 1 if g(G) 7, and a (G) = Δ(G) if g(G) 16 and Δ(G) 3. For series-parallel graphs G, we have a (G) Δ(G) + 1.

关键词： acyclic coloring planar graph girth series-parallel graph

Cloud-based parallel power flow calculation using resilient distributed datasets and directed acyclic graph

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Journal of Modern Power Systems and Clean Energy 2019年第1期7卷 65-77页

作者： Dewen WANG Fangfang ZHOU Jiangman LI School of Control and Computer Engineering North China Electric Power University

With the integration of distributed generation and the construction of cross-regional long-distance power grids, power systems become larger and more *** require faster computing speed and better scalability for power flow calculations to support unit *** on the analysis of a variety of parallelization methods, this paper deploys the large-scale power flow calculation task on a cloud computing platform using resilient distributed datasets(RDDs).It optimizes a directed acyclic graph that is stored in the RDDs to solve the low performance problem of the MapReduce *** paper constructs and simulates a power flow calculation on a large-scale power system based on standard IEEE test *** are conducted on Spark cluster which is deployed as a cloud computing *** show that the advantages of this method are not obvious at small scale, but the performance is superior to the stand-alone model and the MapReduce model for large-scale *** addition, running time will be reduced when adding cluster *** not tested under practical conditions, this paper provides a new way of thinking about parallel power flow calculations in large-scale power systems.

关键词： Power flow calculation Parallel programming model Distributed memory-shared model Resilient distributed datasets(RDDs) Directed acyclic graph(DAG)

Nickel(Ⅱ)-catalyzed asymmetric alkylation of acyclic oxocarbenium ions with carboxylic acid derivatives

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Chinese Chemical Letters 2021年第3期32卷 1237-1240页

作者： Pengbo Ye Xuan Liu Gang Wang Lei Liu School of Chemistry and Chemical Engineering Shandong UniversityJi'nan 250100China

A nickel(Ⅱ)-catalyzed asymmetric alkylation of acyclic oxocarbenium ions generated in situ from corresponding acetals with carboxylic acid derivatives to prepareβ-alkoxyl carbonyl moieties with diverseα-substituents has been *** method exhibited broad scope of acetals and carboxylic acid derivatives with excellent enantioselectivity and good functional group compatibility,and can be conducted in a gram-scale without obvious loss of efficiency.

关键词： Oxocarbenium ion acyclic Nickel Asymmetric catalysis Alkylation

Symmetrical acyclic Aryl Aldazines with Antibacterial and Antifungal Activity

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Pharmacology & Pharmacy 2011年第1期2卷 1-9页

作者： Vanya B. Kurteva Svilen P. Simeonov Margarita Stoilova-Disheva 不详

A series of 22 symmetrical acyclic aromatic aldazines were obtained and their qualitative antimicrobial activities were evaluated against 10 bacterial and 3 fungal species. The results demonstrated that the bi- and polycyclic aromatics studied are remarkably more active than benzaldazines. The latter possess antibacterial activities only, which were dramatically reduced by the introduction of substituents. The tests showed that the activities are strongly dependent on the type and position of the substituents and that the effects on antibacterial and antifungal activities are the opposite. 2-Naphtaldazine was significantly more active than its position isomer 1-naphthaldazine against Saccharomyces cerevisiae and Penicillium chrysogenum, whereas both compounds possess commensurable activities towards Candida tropicalis and the bacterial strains. From the other side, the presence of 4-hydroxy substituent in 1-naphthaldazine reduced the antibacterial and increased the antifungal activities, while the influence of 2-hydroxy group led to reversed results.

关键词： Symmetrical acyclic Aryl Aldazines Synthesis Antibacterial Activity Antifungal Activity

β-acyclic based on extended strict confilict-free

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Journal of Harbin Institute of Technology(New Series) 2000年第4期7卷 34-37页

作者：刘文远郝忠孝王亚东

Introduces the concepts of strict conflict free and extended strict conflict free,proves decomposition satisfies lossless join,keep dependency, β acyclic and 4NF if and only if Γ is extended strict conflict free in the mixed environment,proposes the algorithm of getting degenerated MVDS sets,judging conflict free,judging stric conflict free and β acyclic decomposition in mixed environment,and illustrates with an example that the complexity of algorithm is linear.

关键词： mixed dependency β acyclic scheme decomposition

A Note on acyclic Edge Colouring of Star Graph Families

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American Journal of Computational Mathematics 2015年第3期5卷 253-257页

作者： P. Shanasbabu A. V. Chithra Department of Mathematics National Institute of Technology Calicut India

A proper edge colouring f of a graph G is called acyclic if there are no bichromatic cycles in the graph. The acyclic edge chromatic number or acyclic chromatic index, denoted by , is the minimum number of colours in an acyclic edge colouring of G. In this paper, we discuss the acyclic edge colouring of middle, central, total and line graphs of prime related star graph families. Also exact values of acyclic chromatic indices of such graphs are derived and some of their structural properties are discussed.

关键词： acyclic Edge Colouring acyclic Chromatic Index Middle Graph Central Graph Total Graph Line Graph

Further Results on acyclic Chromatic Number

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Open Journal of Discrete Mathematics 2013年第2期3卷 97-100页

作者： P. Shanas Babu A. V. Chithra Department of Mathematics National Institute of Technology (NIT) Calicut India

An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of *** purpose of this paper is to derive exact values of acyclic chromatic number ... 详细信息

关键词： acyclic Coloring acyclic Chromatic Number Central Graph Middle Graph Total Graph

The 4-acyclic Edge Coloring of Graphs with Large Girths

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Journal of Applied Mathematics and Physics 2015年第12期3卷 1594-1598页

作者： Yuwen Wu Yan Xia School of Information Beijing Wuzi University Beijing China Institute of Policy and Management Chinese Academy of Sciences Beijing China

A proper edge coloring of a graph is acyclic, if every cycle of the graph has at least 3 colors. Let r be a positive integer. An edge coloring is r-acyclic if it is proper and every cycle C has at least ?colors. The r-acyclic edge chromatic ??number of a graph G?is the minimum number of colors needed for any r-acyclic edge coloring of G. When r=4, the result of this paper is that the 4-acyclic chromatic number of a graph with maximum degree Δ and girth ?is less than 18Δ. Furthermore, if the girth of graph G?is at least , then .

关键词： Girth Edge Coloring acyclic Edge Coloring Lovászlocal Lemma