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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
Very good product
Size: Medium, Color: (001) Black / Black / Pitch Gray
I purchased these to wear inside lowcut slip on casual shoes, I don't particularly like to not wear socks in my shoes for hygienic reasons. Prior to purchasing these socks, all I could find were those made of very light beige hosiery type material , and my slip on shoes would slide around a bit. These are light weight and breathable athletic type material, with a very good gripper strip at the heel. One pair of my slip on casual shoes have a particularly lower cut in the toe area, but the shoe is black and I chose the black color and though I see a hint of the sock there, it matches and does not detract from the look of the casual solid black shoe
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Reviewed in the United States on May 15, 2026
★★★★★ 5
They stay out! No more sock wads!
Size: Medium, Color: (100) White / White / Mod Gray
Best no show socks ever made!!!!! I've been struggling for 2 years to find ones that actually stay on your foot, even other national brands, and I just became content wearing my sneakers without socks. They ALWAYS slid down into my show & I ended up walking on a wad of sock until I could fix it...or usually just took them off after a couple of tries. Enter Under Armor!!! They a mid weight, but not very thick & still breathable. They work too by actually staying on your foot! Not once have they slid down into my show!! Very comfortable but they could be a little more affordable.
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Reviewed in the United States on August 1, 2025
★★★★★ 5
Love!
Size: Large, Color: (100) White / White / Mod Gray
Ive tried so many no show socks but I love these. This is the 3rd set I've bought. They never slip off and the material is thin and breathable. Perfect for working out.
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Reviewed in the United States on March 2, 2026
★★★★★ 5
True no-show socks that don’t slide down!
Size: Medium, Color: (100) White / White / Mod Gray, Size: Medium, Color: (100) White / White / Mod Gray
This is the first pair of no-show socks I’ve tried that actually don’t slide down into my shoes. Trust me… I have tried lots of different pairs and this is the one! They fit perfectly. They’re not too thick and they’re obviously durable because I wash them after each wear, so daily.
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Reviewed in the United States on March 21, 2026
★★★★★ 4
Great fit but expensive
Size: Medium, Color: (252) Blush Beige / White / Castlerock
These are really great socks. I love them, but they are definitely pricey.
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Reviewed in the United States on March 30, 2026