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Covering Walks in Graphs

  • Book
  • © 2014

Overview

Authors:
  1. Futaba Fujie

    1. Graduate School of Mathematics, Nagoya University, Nagoya, Japan

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    You can also search for this author in PubMed   Google Scholar

  2. Ping Zhang

    1. Department of Mathematics, Western Michigan University, Kalamazoo, USA

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    You can also search for this author in PubMed   Google Scholar

  • Provides a comprehensive treatment on measures of Hamiltonicity and traversability in graphs
  • Contains intriguing open problems and conjectures on spanning walks in graphs
  • Describes new frame works for several well-known Hamiltonian concepts with interesting new results
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Eulerian Walks

    • Futaba Fujie, Ping Zhang
    Pages 1-33

  3. Hamiltonian Walks

    • Futaba Fujie, Ping Zhang
    Pages 35-66

  4. Traceable Walks

    • Futaba Fujie, Ping Zhang
    Pages 67-104

  5. Back Matter

    Pages 105-110
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Keywords

About this book

Covering Walks  in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and Hamiltonian concepts are examined. Describes several variations of traceable numbers, which provide new frame works for several well-known Hamiltonian concepts and produce interesting new results.

Reviews

From the book reviews:

“Fujie (Nagoya Univ., Japan) and Zhang (Western Michigan Univ.) broadly survey many similar statements, some theorems, and some conjectures in a manner clear enough for beginners and thorough enough for experts. … Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (3), November, 2014)

Authors and Affiliations

  • Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Futaba Fujie

  • Department of Mathematics, Western Michigan University, Kalamazoo, USA

    Ping Zhang

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