Covering Walks in Graphs

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Springer Science & Business Media, Jan 25, 2014 - Mathematics - 110 pages
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.
 

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Contents

1 Eulerian Walks
1
2 Hamiltonian Walks
35
3 Traceable Walks
67
References
105
Index
108
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About the author (2014)

Dr. Ping Zhang is a Licensed Acupuncturist, a National Certified Herbalist, with a PhD in Oriental Medicine. She has more than 20 years of clinical experience specializing in facial and body rejuvenation acupuncture, acupressure, and Chinese herbal medicine. As the first recipient of a PhD in Oriental Medicine in the US, Dr. Zhang is a pioneer in the field of Traditional Chinese Medicine anti-aging and facial and body rejuvenation. She designed and taught the first ever graduate level course in the U.S. on Traditional Chinese Medicine facial and body rejuvenation for New York College for the Health Professions. She is the author of the books 'Anti-Aging Therapy' and 'A Comprehensive Handbook for Traditional Chinese Medicine Facial Rejuvenation' which are published and sold internationally. Dr. Zhang teaches and lectures on facial and body rejuvenation techniques to beauty and medical professionals and students around the world.

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