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Description
Fractional Graph Theory: A Rational Approach to the Theory of GraphsA unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid
A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers, and fractional aspects of partially ordered sets.Challenging exercises reinforce the contents of each chapter, and the authors provide substantial references and bibliographic materials. A comprehensive reference for researchers, this volume also constitutes an excellent graduate-level text for students of graph theory and linear programming.
Binding Type: Paperback
Publisher: Dover Publications
Published: 11/16/2011
ISBN: 9780486485935
Pages: 211
Weight: 0.65lbs
Size: 8.90h x 5.90w x 0.60d
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★★★★★ 5
Good for receding gums
Size: 4 Ounce (Pack of 1)
I use this Boka toothpaste daily and it is super sensitive on my receding gums. It has a subtle flavor, and isn't too strong. Highly recommend if you have sensitive teeth.
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Reviewed in the United States on May 10, 2026
★★★★★ 5
Buy this stuff!
Size: 4 Ounce (Pack of 1)
Smooth flavor, really good, no chemical aftertaste.
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Reviewed in the United States on May 25, 2026
★★★★★ 4
Makes my sensitive teeth have a magical shield
Size: 4 Ounce (Pack of 1)
I've been using the Boku sensitive toothpaste twice a day for almost 2 months now and it's definitely improved my tooth sensitivity since I first started. I used to have to be extra careful about what I ate or drank, specially while out in the cold because the pain I felt was unbearable. Now it's like a magical coating is protecting them because it's barely noticable anymore. I also really like that it doesn't taste bad, and it leaves my teeth looking a few shades lighter and my breath stays pretty fresh for a decent amount of time after using. The only thing I would change is the consistency because it's a lil thin and kinda flings everywhere on my spin brush but that isn't enough to make me dislike it.
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Reviewed in the United States on April 28, 2026
★★★★★ 5
Works amazing! Worth the price!
Size: 4 Ounce (Pack of 1)
I absolutely love this toothpaste, I read an article where you can 100% use it with your Sensodyne or Colgate sensitivity toothpaste to get the sensitivity benefit from that as well as the remineralizing from this toothpaste. I didn’t notice a texture difference at all, the taste was good, I will definitely be buying this again. I used it with David’s coconut oil pulling and my teeth feel amazing, no sensitivity to cold or hot anymore! Buy it yesterday you won’t be disappointed
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Reviewed in the United States on May 20, 2026
★★★★★ 5
Not super strong
Size: 4 Ounce (Pack of 1)
This is the stuff I reach for. It’s mild enough where I don’t feel like people around me can smell inside my mouth. But still powerful enough where my mouth feels fresh. Good for my sensitive teeth too. Very helpful
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Reviewed in the United States on May 25, 2026