Bjarne Toft's Books

Hex

The Full Story

By: Ryan B. Hayward,Bjarne Toft

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Hex

The Full Story

By: Ryan B. Hayward,Bjarne Toft

Hex is the subject of books by Martin Gardner and Cameron Browne. Hex theory touches on graph theory, game theory and combinatorial game theory, with elegant proofs that the game has no draws and that the first player can win. From machines built by Claude Shannon to agents using Monte Carlo Tree Search, Hex is often used in the study of artificial intelligence. Written for a wide audience, this is the full story of Hex, inside and out, with all its twists and turns: Hein’s creation, Lindhard’s puzzles, Nash’s proofs, Gale’s Bridg-it, the game of Rex, Shannon’s machines, Bridg-it’s fall, Hex’s resilience, Hex theory, the hunt for winning strategies, and the rise of Hexbots.

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Page Count

299

Publisher

CRC Press

Published Date

ISBN 10

0429627696

ISBN 13

9780429627699

Brooks' Theorem

Graph Coloring and Critical Graphs

By: Michael Stiebitz,Thomas Schweser,Bjarne Toft

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Brooks' Theorem

Graph Coloring and Critical Graphs

By: Michael Stiebitz,Thomas Schweser,Bjarne Toft

Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory -- it is mentioned/treated in all general monographs on graph theory. It has sparked research in several directions. This book presents a comprehensive overview of this development and see it in context. It describes results, both early and recent, and explains relations: the various proofs, the many extensions and similar results for other graph parameters. It serves as a valuable reference to a wealth of information, now scattered in journals, proceedings and dissertations. The reader gets easy access to this wealth of information in comprehensive form, including best known proofs of the results described. Each chapter ends in a note section with historical remarks, comments and further results. The book is also suitable for graduate courses in graph theory and includes exercises. The book is intended for readers wanting to dig deeper into graph coloring theory than what is possible in the existing book literature. There is a comprehensive list of references to original sources.

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Page Count

663

Publisher

Springer Nature

Published Date

ISBN 10

3031500652

ISBN 13

9783031500657

Graph Coloring Problems

By: Tommy R. Jensen,Bjarne Toft

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Graph Coloring Problems

By: Tommy R. Jensen,Bjarne Toft

Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.

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Page Count

320

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030745

ISBN 13

9781118030745

Graph Edge Coloring

Vizing's Theorem and Goldberg's Conjecture

By: Michael Stiebitz,Diego Scheide,Bjarne Toft,Lene M. Favrholdt

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Graph Edge Coloring

Vizing's Theorem and Goldberg's Conjecture

By: Michael Stiebitz,Diego Scheide,Bjarne Toft,Lene M. Favrholdt

Features recent advances and new applications in graph edgecoloring Reviewing recent advances in the Edge Coloring Problem, GraphEdge Coloring: Vizing's Theorem and Goldberg's Conjectureprovides an overview of the current state of the science,explaining the interconnections among the results obtained fromimportant graph theory studies. The authors introduce many newimproved proofs of known results to identify and point to possiblesolutions for open problems in edge coloring. The book begins with an introduction to graph theory and theconcept of edge coloring. Subsequent chapters explore importanttopics such as: Use of Tashkinov trees to obtain an asymptotic positive solutionto Goldberg's conjecture Application of Vizing fans to obtain both known and newresults Kierstead paths as an alternative to Vizing fans Classification problem of simple graphs Generalized edge coloring in which a color may appear more thanonce at a vertex This book also features first-time English translations of twogroundbreaking papers written by Vadim Vizing on an estimate of thechromatic class of a p-graph and the critical graphs within a givenchromatic class. Written by leading experts who have reinvigorated research inthe field, Graph Edge Coloring is an excellent book formathematics, optimization, and computer science courses at thegraduate level. The book also serves as a valuable reference forresearchers interested in discrete mathematics, graph theory,operations research, theoretical computer science, andcombinatorial optimization.

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Page Count

344

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118205561

ISBN 13

9781118205563

The Frozen Saqqaq Sites of Disko Bay, West Greenland - Qeqertasussuk and Qajaa (2400-900 BC)

Studies of Saqqaq Material Culture in an Eastern Arctic Perspective

By: Bjarne Grønnow

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The Frozen Saqqaq Sites of Disko Bay, West Greenland - Qeqertasussuk and Qajaa (2400-900 BC)

Studies of Saqqaq Material Culture in an Eastern Arctic Perspective

By: Bjarne Grønnow

Qeqertasussuk and Qajaa are the only known sites of the Early Arctic Small Tool tradition in the Eastern Arctic, where all kinds of organic materials - wood, bone, baleen, hair, skin - are preserved in permafrozen culture layers. Together, the sites cover the entire Saqqaq era in Greenland (c. 2400-900 BC). Technological and contextual analyses of the excellently preserved archaeological materials from the frozen layers form the core of this publication. Bjarne Grønnow draws a new picture of a true Arctic pioneer society with a remarkably complex technology. The Saqqaq hunting tool kit, consisting of bows, darts, lances, harpoons, and throwing boards as well as kayak-like sea-going vessels, is described for the first time. A wide variety of hand tools and household utensils as well as lithic and organic refuse and animal bones were found on the intact floor of a midpassage dwelling at Qeqertasussuk. These materials provide entirely new information on the daily life and subsistence of the earliest hunting groups in Greenland. Comparative studies put the Saqqaq Culture into a broad cultural-historical perspective as one of the pioneer societies of the Eastern Arctic.

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Page Count

495

Publisher

Museum Tusculanum Press

Published Date

ISBN 10

8763545616

ISBN 13

9788763545617

Brooks' Theorem

Graph Coloring and Critical Graphs

By: Michael Stiebitz,Thomas Schweser,Bjarne Toft

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Brooks' Theorem

Graph Coloring and Critical Graphs

By: Michael Stiebitz,Thomas Schweser,Bjarne Toft

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Page Count

663

Publisher

Springer Nature

Published Date

ISBN 10

3031500652

ISBN 13

9783031500657

Hex

The Full Story

By: Ryan B. Hayward,Bjarne Toft

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Hex

The Full Story

By: Ryan B. Hayward,Bjarne Toft

Hex: The Full Story is for anyone - hobbyist, professional, student, teacher - who enjoys board games, game theory, discrete math, computing, or history. hex was discovered twice, in 1942 by Piet Hein and again in 1949 by John F. nash. How did this happen? Who created the puzzle for Hein's Danish newspaper column? How are Martin Gardner, David Gale, Claude Shannon, and Claude Berge involved? What is the secret to playing Hex well? The answers are inside... Features New documents on Hein's creation of Hex, the complete set of Danish puzzles, and the identity of their composer Chapters on Gale's game Bridg-it, the game Rex, computer Hex, open Hex problems, and more Dozens of new puzzles and solutions Study guide for Hex players Supplemenetary text for a course in game theory, discrete math, computer science, or science history

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Page Count

320

Publisher

CRC Press

Published Date

ISBN 10

0429629338

ISBN 13

9780429629334

Graph Coloring Problems

By: Tommy R. Jensen,Bjarne Toft

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Graph Coloring Problems

By: Tommy R. Jensen,Bjarne Toft

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Page Count

320

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030745

ISBN 13

9781118030745

Hex, Inside and Out

The Full Story

By: Ryan B. Hayward,Bjarne Toft

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Hex, Inside and Out

The Full Story

By: Ryan B. Hayward,Bjarne Toft

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Solve jigsaw puzzle

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Page Count

298

Publisher

CRC Press

Published Date

ISBN 10

0429031963

ISBN 13

9780429031960

Book's by Bjarne Toft

Hex

Hex

Brooks' Theorem

Brooks' Theorem

Graph Coloring Problems

Graph Coloring Problems

Graph Edge Coloring

Graph Edge Coloring

The Frozen Saqqaq Sites of Disko Bay, West Greenland - Qeqertasussuk and Qajaa (2400-900 BC)

The Frozen Saqqaq Sites of Disko Bay, West Greenland - Qeqertasussuk and Qajaa (2400-900 BC)

Brooks' Theorem

Brooks' Theorem

Hex

Hex

Graph Coloring Problems

Graph Coloring Problems

Hex, Inside and Out

Hex, Inside and Out

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