Combinatorics and Graph Theory
Springer Science & Business Media, 19. 7. 2000 - 228 strán (strany)
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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2-coloring algorithm appears apply arrangements assignment assume atoms axiom beads binomial blue bound called cardinal Chapter choice Claim coefficients collection color combinatorics complete components compute connected consider consists construct contains contradiction count cycle defined definition denote determine edges elements equivalence exactly example Exercise exists fact Figure finite five formula four function Given gives graph G hand holds identity implies induction infinite integer kind labeled least Lemma Let G matching Mathematics Note objects obtain ordinal pair particular path perfect matching permutation pigeonhole pigeons planar positive possible prefers problem proof properties proposers prove Ramsey regular relation represent representation result sequence Show stable statement step subgraph subset Suppose Theorem tree vertex vertices well-ordered
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