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出版者:高等教育出版社

作者:于青林//刘桂真

出品人:

页数:353

译者:

出版时间:2009-7

价格:69.00元

装帧:

isbn号码:9787040257588

丛书系列:组合数学丛书

图书标签:

图论
因子图
匹配
可扩性
组合优化
网络流
算法
图算法
离散数学
数学规划

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具体描述

《图的因子和匹配可扩性》讲述了：Graph theory is one of the branches of modern mathematics which has shown impressive ad vances in recet years.An explosive growth of graph theory is witnessed due to its essential roles providing structural and indispens-able tools in computer science,communication networks and combinatorial optimization problems.

这本书系统地探讨了图的因子分解与匹配在现代计算中的重要作用。它深入分析了如何通过理解图结构的各类因子关系，从而实现更高效的算法设计和实际应用。这本书着重介绍了多种方法，从基础概念到高级技术，全面覆盖了图理论在数据处理、优化问题以及复杂网络分析中的关键作用。作者将内容细致展开，详细解析了图因子分解的基本原理，并结合实际案例说明其应用场景。例如，通过深入讲解图匹配算法的机制，读者能够掌握如何在复杂系统中找到最佳匹配方案，从而提升解决问题的效率。书中还引入了最新的研究成果与技术趋势，使内容既有理论深度又富有实践指导。整个书籍强调图结构的灵活性和可扩展性，帮助读者理解如何将因子分析应用于各种实际问题，如社交网络、交通系统、资源分配等。这些内容不仅具有较高的学术价值，也对从业者提供了切实可行的参考。书中还特别注重解释复杂概念，确保每个章节都易于理解，同时不遗漏关键细节。无论是初学者还是有一定背景的专业人士，都能从中获得有价值的知识和技能。通过系统化的内容设计，这本书旨在成为图计算领域的重要参考资料。读者将深入了解因子分解与匹配技术的原理及其实现路径，进一步提升对复杂图问题的分析能力。这一书不仅填补了理论与实践之间的空白，还为后续研究和应用提供了坚实基础。整体结构清晰、内容丰富，适合那些希望深入探索图计算领域的人士阅读。总体来说，这是一本完整且深度的图理论学习资源，它不仅呈现了经典理论，也结合现代应用，为读者提供全方位的知识支持。通过细致的分析和实际案例，书中详实地展示了图因子与匹配在不同领域的重要作用，值得专业人士仔细研读。

作者简介

Dr.Yu is a professor in the Department of Mathematics and Statistics at the Thompson Rivers University of Canada.His research interests include graph theory and combinatorial optimization.

Dr.Liu is a professor in the School of Mathematics at Shandong University of China.Her research interests include graph theory and matroid theory.

目录信息

1 Matchings and Perfect Matchings 1.1 Definitions and terminologies 1.2 Matchings in bipartite graphs and augmenting path 1.3 Matchings in non-bipartite graphs 1.4 Sufficient conditions for 1-factors 1.5 Gallai-Edmonds Structure Theorem 1.6 Number of 1-factors2 Degree Constraint Factors 2.1 Characterizations of factors 2.2 Factors in bipartite graphs 2.3 Factors with special properties 2.4 L-factor3 Factors and Graphic Parameters 3.1 Toughness and k-factors 3.2 Toughness and [a，b]-factors 3.3 Binding number and factors 3.4 Connectivity and factors 3.5 Other parameters and existence of factors4 Component Factors and Connected Factors 4.1 Star factor 4.2 Path and cycle factors 4.3 El-Zahar's Conjecture and other component factors 4.4 Connected [a，b]-factors 4.5 Connected (g，f)-factors 4.6 Generalized trees5 Elementary Graphs and Decomposition Theory 5.1 Elementary graphs and 1-extendable graphs 5.2 Ear decomposition 5.3 Minimal graphs and more decompositions 5.4 Bricks and optimal ear decomposition6 k-Extendable Graphs and n-Factor-Critical Graphs 6.1 Characterizations and basic properties 6.2 Equivalence and recursive relationships 6.3 Matching extension and graphic parameters 6.3.1 Matching extension and forbidden subgraphs 6.3.2 Matching extension and toughness 6.3.3 Matching extension in planar graphs and surfaces 6.3.4 Matching extension，degree sum and closure operations 6.3.5 Matching extension and product of graphs 6.3.6 Matching extension and other parameters 6.4 Extendability of symmetric graphs7 Extremal k-Extendable Graphs and Generalizations 7.1 Maximal and minimal k-extendable graphs 7.2 Generalization of matching extension 7.3 Variations of graph extension8 Fractional Factors of Graphs 8.1 Fractional matchings 8.2 Fractional (g，f)-factors 8.3 Parameters and fractional factors of graphs 8.4 Maximum and minimum fractional (g，f)-factors 8.5 Connected fractional factorsIndexReferences
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