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Fractional Graph Theory By Edward R. Scheinerman and Daniel H. Ullman
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About this book :-
Fractional Graph Theory
Edward R. Scheinerman, Daniel H. Ullman .
Professors Scheinerman and Ullman developed general fractional theory of hypergraphs and move on to provide in-depth coverage of basic and advanced topics which are include fractional matching, fractional coloring, fractional arboricity via matroid methods.
Book Detail :-
Title: Fractional Graph Theory
Edition:
Author(s): Edward R. Scheinerman, Daniel H. Ullman
Publisher:
Series:
Year: 2008
Pages: 167
Type: PDF
Language: English
ISBN:
Country: US
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Book Contents :-
Fractional Graph Theory
Edward R. Scheinerman, Daniel H. Ullman
cover the following topics.
1. General Theory: Hypergraphs
1.1 Hypergraph covering and packing
1.2 Fractional covering and packing
1.3 Some consequences
1.4 A game-theoretic approach
1.5 Duality and duality
1.6 Asymptotic covering and packing
1.7 Exercises
1.8 Notes
2. Fractional Matching
2.1 Introduction
2.2 Results on maximum fractional matchings
2.3 Fractionally Hamiltonian graphs
2.4 Computational complexity
2.5 Exercises
2.6 Notes
3. Fractional Coloring
3.1 Definitions
3.2 Homomorphisms and the Kneser graphs
3.3 The duality gap
3.4 Graph products
3.5 The asymptotic chromatic and clique numbers
3.6 The fractional chromatic number of the plane
3.7 The Erd?os-Faber-Lov´asz conjecture
3.8 List coloring
3.9 Computational complexity
3.10 Exercises
3.11 Notes
4. Fractional Edge Coloring
4.1 Introduction
4.2 An exact formula
4.3 The matching polytope
4.4 Proof and consequences
4.5 Computational complexity
4.6 Fractional total chromatic number
4.7 Exercises
4.8 Notes
5. Fractional Arboricity and Matroid Methods
5.1 Arboricity and maximum average degree
5.2 Matroid theoretic tools
5.3 Matroid partitioning
5.4 Arboricity again
5.5 Maximum average degree again
5.6 Duality, duality, duality, and edge toughness
5.7 Exercises
5.8 Notes
6. Fractional Isomorphism
6.1 Relaxing isomorphism
6.2 Linear algebra tools
6.3 Equitable partitions
6.4 Iterated degree sequences
6.5 The main theorem
6.6 Other relaxations of isomorphism
6.7 Exercises
6.8 Notes
7. Fractional Odds and Ends
7.1 Fractional topological graph theory
7.2 Fractional cycle double covers
7.3 Fractional Ramsey theory
7.4 Fractional domination
7.5 Fractional intersection number
7.6 Fractional dimension of a poset
7.7 Sperner’s theorem: a fractional perspective
7.8 Exercises
7.9 Notes
A Background
A.1 Basic graph theory and notation
A.2 Hypergraphs, multigraphs, multisets, fuzzy sets
A.3 Linear programming
A.4 The subadditivity lemma
A.5 Exercises
A.6 Notes
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