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GRAPH THEORY AND DECOMPOSITION.

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...

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Bibliographic Details
Main Author: Kottarathil, Jomon
Corporate Author: Taylor & Francis
Other Authors: Naduvath, Sudev, Kureethara, Joseph Varghese
Format: eBook
Language:English
Published: [S.l.] : CHAPMAN & HALL CRC, 2024.
Subjects:
Graph theory.
Decomposition (Mathematics)
Décomposition (Mathématiques)
MATHEMATICS / Discrete Mathematics
MATHEMATICS / Applied
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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