Formatas: Paperback / softback, 110 pages, aukštis x plotis: 235x155 mm, weight: 2226 g, 11 Illustrations, color; 26 Illustrations, black and white; XIV, 110 p. 37 illus., 11 illus. in color., 1 Paperback / softback
Formatas: Paperback / softback, 110 pages, aukštis x plotis: 235x155 mm, weight: 2226 g, 11 Illustrations, color; 26 Illustrations, black and white; XIV, 110 p. 37 illus., 11 illus. in color., 1 Paperback / softback
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 K nigsberg 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.
Recenzijos
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)
1 Eulerian Walks
1
(34)
1.1 The Konigsberg Bridge Problem
1
(7)
1.2 Eulerian Graphs
8
(16)
1.3 Graphs with Odd Vertices
24
(3)
1.4 The Chinese Postman Problem
27
(4)
1.5 Randomly Eulerian Graphs
31
(4)
2 Hamiltonian Walks
35
(32)
2.1 The Icosian Game
35
(3)
2.2 Hamiltonian Graphs
38
(6)
2.3 The Toughness of a Graph
44
(2)
2.4 The Traveling Salesman Problem
46
(1)
2.5 Line Graphs and Powers of Graphs
47
(4)
2.6 Hamiltonian Walks and Cyclic Orderings
51
(7)
2.7 The Upper Hamiltonian Number of a Graph
58
(4)
2.8 The Hamiltonian Spectrum of a Graph
62
(5)
3 Traceable Walks
67
(38)
3.1 The Traceable Number of a Graph
67
(4)
3.2 The Traceable Number of a Tree
71
(3)
3.3 The Traceable and Hamiltonian Numbers of a Graph
74
(4)
3.4 The Upper Traceable Number of a Graph
78
(6)
3.5 Traceable Numbers of Vertices in a Graph
84
(3)
3.6 The Maximum Vertex Traceable Number of a Graph
