圖的因子和匹配可擴性 pdf epub mobi txt 電子書下載在線閱讀 2026

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出版者:高等教育齣版社

作者:於青林//劉桂真

出品人:

頁數:353

译者:

出版時間:2009-7

價格:69.00元

裝幀:

isbn號碼:9787040257588

叢書系列:組閤數學叢書

圖書標籤:

圖論
因子圖
匹配
可擴性
組閤優化
網絡流
算法
圖算法
離散數學
數學規劃

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具體描述

《圖的因子和匹配可擴性》講述瞭：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.

這本書係統地探討瞭圖的因子分解與匹配在現代計算中的重要作用。它深入分析瞭如何通過理解圖結構的各類因子關係，從而實現更高效的算法設計和實際應用。這本書著重介紹瞭多種方法，從基礎概念到高級技術，全麵覆蓋瞭圖理論在數據處理、優化問題以及復雜網絡分析中的關鍵作用。作者將內容細緻展開，詳細解析瞭圖因子分解的基本原理，並結閤實際案例說明其應用場景。例如，通過深入講解圖匹配算法的機製，讀者能夠掌握如何在復雜係統中找到最佳匹配方案，從而提升解決問題的效率。書中還引入瞭最新的研究成果與技術趨勢，使內容既有理論深度又富有實踐指導。整個書籍強調圖結構的靈活性和可擴展性，幫助讀者理解如何將因子分析應用於各種實際問題，如社交網絡、交通係統、資源分配等。這些內容不僅具有較高的學術價值，也對從業者提供瞭切實可行的參考。書中還特彆注重解釋復雜概念，確保每個章節都易於理解，同時不遺漏關鍵細節。無論是初學者還是有一定背景的專業人士，都能從中獲得有價值的知識和技能。通過係統化的內容設計，這本書旨在成為圖計算領域的重要參考資料。讀者將深入瞭解因子分解與匹配技術的原理及其實現路徑，進一步提升對復雜圖問題的分析能力。這一書不僅填補瞭理論與實踐之間的空白，還為後續研究和應用提供瞭堅實基礎。整體結構清晰、內容豐富，適閤那些希望深入探索圖計算領域的人士閱讀。總體來說，這是一本完整且深度的圖理論學習資源，它不僅呈現瞭經典理論，也結閤現代應用，為讀者提供全方位的知識支持。通過細緻的分析和實際案例，書中詳實地展示瞭圖因子與匹配在不同領域的重要作用，值得專業人士仔細研讀。

作者簡介

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.

目錄資訊

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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