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GRAPH THEORY AND DECOMPOSITION
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: [S.l.] : CHAPMAN & HALL CRC, 2024Beschreibung: 1 Online-RessourceISBN:- 9781040018736
- 1040018734
- 9781003391678
- 1003391672
- 9781040018767
- 1040018769
- 1032489235
- 9781032489230
- 511/.5 23/eng/20240304
- QA166
Inhalte:
Zusammenfassung: The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theoryPPN: PPN: 1907958177Package identifier: Produktsigel: ZDB-4-NLEBK | BSZ-4-NLEBK-KAUB
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- About the Authors -- Symbols -- 1. Decompositions of Graphs: An Introduction -- 1.1. The Early Developments of Concepts of Decompositions -- 1.2. Basic Terminologies -- 1.2.1. Digraphs -- 1.2.2. Block Designs -- I. Decompositions into Cyclic Graphs -- 2. Cycle Decompositions -- 2.1. Cm-Decompositions -- 2.1.1. Decomposition of Kn into m-Cycles and a Perfect Matching -- 2.2. Cycles of Varying Lengths -- 2.3. Hamilton Decompositions -- 2.4. Hajós' Conjecture -- 2.5. Open Problems -- 3. Digraph Decompositions
3.1. Hamilton Directed Graph Decompositions -- 3.2. Cycles of Varying Lengths -- 3.3. Bermond-Thomassen Conjecture -- 3.4. Lichiardopol's Conjecture -- 3.5. Kelly's Conjecture -- 3.6. Some Other Conjectures on Digraphs -- 3.7. Open Problems -- 4. K4 − e Decompositions -- 4.1. Block Design of Graphs -- 4.2. Spectrum of K4 − e Designs -- 4.3. Resolvable K4 − e Designs -- 4.4. Intersection Problem of K4 − e Designs -- 4.5. The K4 − e Designs of Graphs with Small Orders -- 4.5.1. Some Constructions on K4 − e Designs -- 4.6. Open Problems -- II. Decompositions into Acyclic Graphs
5. Tree Decompositions -- 5.1. Treewidth, Pathwidth, and Branchwidth -- 5.2. Some Other Methods -- 5.3. Barát-Thomassen Conjecture -- 5.4. Kotzig-Ringel-Rosa Conjecture -- 5.5. Ringel's Conjecture -- 5.6. Open Problems -- 6. Path Decompositions -- 6.1. Path Number of a Graph -- 6.1.1. Graphoidal Cover -- 6.2. Pk Decompositions -- 6.2.1. P3 Decompositions -- 6.2.2. P4 Decompositions -- 6.2.3. P5 Decompositions -- 6.3. Path Decompositions using Girth -- 6.4. Path Decompositions of Digraphs -- 6.5. Paths of Varying Lengths -- 6.6. Gallai's Conjecture -- 6.7. Open Problems -- 7. Star Decompositions
7.1. Sk Decompositions -- 7.2. Claw-Decompositions -- 7.3. Stars of Varying Lengths -- 7.4. Double Star Decompositions -- 7.5. Star Decompositions of Digraphs -- 7.6. Spectrum and Intersection Problems -- 7.7. Star Number of Graphs -- 7.8. Open Problems -- 8. Pendant Number of Graphs -- 8.1. Pendant Number -- 8.2. Properties of Pendant Number -- 8.3. Equipendant, Selfipendant and Extremal Pendant Graphs -- 8.4. Pendant Number of Line Graphs and Total Graphs -- 8.5. Pendant Number of Some Graph Products -- 8.5.1. Rooted Products -- 8.5.2. Corona Products -- 8.5.3. Cartesian Products
8.5.4. Direct Products -- 8.6. Path-Induced Signed Graphs -- 8.6.1. Path-Induced Signed Graphs -- 8.6.2. Balance in Path-Induced Signed Graphs -- 8.6.3. Pseudo-balancing of Path-Induced Signed Graphs -- 8.6.4. Clusterability in Path-Induced Signed Graphs -- 8.7. Marcin's Algorithm -- 8.8. Open Problems -- III. Decompositions into Multiple Graphs -- 9. Multiple Decompositions of Graphs -- 9.1. Decomposing Graphs into Pairs -- 9.1.1. {Pl, Sk} Decompositions -- 9.1.2. {Cl, Sk} Decompositions -- 9.1.3. {Pl, Ck} Decompositions -- 9.1.4. Complementing Pair (G, G) Decompositions
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