Combinatorics and Graph Theory

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Springer Science & Business Media, Jul 19, 2000 - Mathematics - 228 pages
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Three things should be considered: problems, theorems, and applications. - Gottfried Wilhelm Leibniz, Dissertatio de Arte Combinatoria, 1666 This book grew out of several courses in combinatorics and graph theory given at Appalachian State University and UCLA in recent years. A one-semester course for juniors at Appalachian State University focusing on graph theory covered most of Chapter 1 and the first part of Chapter 2. A one-quarter course at UCLA on combinatorics for undergraduates concentrated on the topics in Chapter 2 and included some parts of Chapter I. Another semester course at Appalachian State for advanced undergraduates and beginning graduate students covered most of the topics from all three chapters. There are rather few prerequisites for this text. We assume some familiarity with basic proof techniques, like induction. A few topics in Chapter 1 assume some prior exposure to elementary linear algebra. Chapter 2 assumes some familiarity with sequences and series, especially Maclaurin series, at the level typically covered in a first-year calculus course. The text requires no prior experience with more advanced subjects, such as group theory.
 

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Contents

II
1
III
2
V
5
VI
8
VII
12
VIII
13
IX
16
X
20
XLI
115
XLII
117
XLIII
122
XLV
127
XLVI
131
XLVII
133
XLVIII
139
L
142

XI
24
XII
33
XIV
37
XV
39
XVI
42
XVII
44
XVIII
45
XIX
47
XX
52
XXI
56
XXII
59
XXIII
60
XXIV
62
XXV
66
XXVI
69
XXVII
74
XXIX
76
XXX
81
XXXI
84
XXXII
85
XXXIII
86
XXXIV
90
XXXV
96
XXXVI
101
XXXVII
102
XXXVIII
103
XXXIX
106
XL
112
LI
147
LII
149
LIII
153
LIV
155
LV
159
LVI
161
LVII
162
LVIII
165
LIX
169
LX
170
LXI
171
LXII
176
LXIII
179
LXIV
182
LXV
183
LXVI
186
LXVII
190
LXVIII
195
LXIX
196
LXX
197
LXXI
199
LXXII
201
LXXIII
204
LXXIV
206
LXXV
209
LXXVI
211
LXXVII
219
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About the author (2000)

Jeffry L. Hirst has taught at the Ohio State University and Appalachian State University.

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