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Fractional Graph Theory By Edward R. Scheinerman and Daniel H. Ullman

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Fractional Graph Theory written by Edward R. Scheinerman and Daniel H. Ullman . This is an other great mathematics book 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

  • Download Free PDF Fractional Graph Theory By Edward R. Scheinerman and Daniel H. Ullman
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