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1.

図書

図書
John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
出版情報: New York : Springer, c2000  xiii, 225 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Graph Theory: Introductory Concepts
Trees
Planarity
Colorings
Matchings
Ramsey Theory
References
Combinatorics: Three Basic Problems
Binomial Coefficients
The Principle of Inclusion and Exclusion
Generating Functions
Polya's Theory of Counting
More Numbers
Stable Marriage
Infinite Combinatorics and Graph Theory: Pigeons and Trees
Ramsey Revisited
ZFC
The Return of der Koenig
Ordinals, Cardinals, and Many Pigeons
Incompleteness and Coardinals
Weakly Compact Cardinals
Finite Combinatorics with Infinite Consequences
Points of Departure
Graph Theory: Introductory Concepts
Trees
Planarity
2.

図書

図書
Jack E. Graver, Mark E. Watkins
出版情報: New York ; Berlin : Springer, c1977  xx, 351 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 54
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3.

図書

図書
Ioan Tomescu ; translated from Romanian by Robert A. Melter
出版情報: New York : Wiley, c1985  xvii, 335 p. ; 25 cm
シリーズ名: Wiley-Interscience series in discrete mathematics
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4.

図書

図書
Rainer Bodendiek, Rudolf Henn (eds.)
出版情報: Heidelberg : Physica, c1990  xix, 792 p. ; 25 cm
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5.

図書

図書
Even, Shimon, 1935-
出版情報: New York : Macmillan, [1973]  xii, 260 p ; 24 cm
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6.

図書

図書
John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
出版情報: New York, NY : Springer, c2008  xv, 381 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface to the Second Edition
Preface to the First Edition
Graph Theory / 1:
Introductory Concepts / 1.1:
Graphs and Their Relatives / 1.1.1:
The Basics / 1.1.2:
Special Types of Graphs / 1.1.3:
Distance in Graphs / 1.2:
Definitions and a Few Properties / 1.2.1:
Graphs and Matrices / 1.2.2:
Graph Models and Distance / 1.2.3:
Trees / 1.3:
Definitions and Examples / 1.3.1:
Properties of Trees / 1.3.2:
Spanning Trees / 1.3.3:
Counting Trees / 1.3.4:
Trails, Circuits, Paths, and Cycles / 1.4:
The Bridges of Konigsberg / 1.4.1:
Eulerian Trails and Circuits / 1.4.2:
Hamiltonian Paths and Cycles / 1.4.3:
Three Open Problems / 1.4.4:
Planarity / 1.5:
Euler's Formula and Beyond / 1.5.1:
Regular Polyhedra / 1.5.3:
Kuratowski's Theorem / 1.5.4:
Colorings / 1.6:
Definitions / 1.6.1:
Bounds on Chromatic Number / 1.6.2:
The Four Color Problem / 1.6.3:
Chromatic Polynomials / 1.6.4:
Matchings / 1.7:
Hall's Theorem and SDRs / 1.7.1:
The Konig-Egervary Theorem / 1.7.3:
Perfect Matchings / 1.7.4:
Ramsey Theory / 1.8:
Classical Ramsey Numbers / 1.8.1:
Exact Ramsey Numbers and Bounds / 1.8.2:
Graph Ramsey Theory / 1.8.3:
References / 1.9:
Combinatorics / 2:
Some Essential Problems / 2.1:
Binomial Coefficients / 2.2:
Multinomial Coefficients / 2.3:
The Pigeonhole Principle / 2.4:
The Principle of Inclusion and Exclusion / 2.5:
Generating Functions / 2.6:
Double Decks / 2.6.1:
Counting with Repetition / 2.6.2:
Changing Money / 2.6.3:
Fibonacci Numbers / 2.6.4:
Recurrence Relations / 2.6.5:
Catalan Numbers / 2.6.6:
Polya's Theory of Counting / 2.7:
Permutation Groups / 2.7.1:
Burnside's Lemma / 2.7.2:
The Cycle Index / 2.7.3:
Polya's Enumeration Formula / 2.7.4:
de Bruijn's Generalization / 2.7.5:
More Numbers / 2.8:
Partitions / 2.8.1:
Stirling Cycle Numbers / 2.8.2:
Stirling Set Numbers / 2.8.3:
Bell Numbers / 2.8.4:
Eulerian Numbers / 2.8.5:
Stable Marriage / 2.9:
The Gale-Shapley Algorithm / 2.9.1:
Variations on Stable Marriage / 2.9.2:
Combinatorial Geometry / 2.10:
Sylvester's Problem / 2.10.1:
Convex Polygons / 2.10.2:
Infinite Combinatorics and Graphs / 2.11:
Pigeons and Trees / 3.1:
Ramsey Revisited / 3.2:
ZFC / 3.3:
Language and Logical Axioms / 3.3.1:
Proper Axioms / 3.3.2:
Axiom of Choice / 3.3.3:
The Return of der Konig / 3.4:
Ordinals, Cardinals, and Many Pigeons / 3.5:
Cardinality / 3.5.1:
Ordinals and Cardinals / 3.5.2:
Pigeons Finished Off / 3.5.3:
Incompleteness and Cardinals / 3.6:
Godel's Theorems for PA and ZFC / 3.6.1:
Inaccessible Cardinals / 3.6.2:
A Small Collage of Large Cardinals / 3.6.3:
Weakly Compact Cardinals / 3.7:
Infinite Marriage Problems / 3.8:
Hall and Hall / 3.8.1:
Countably Many Men / 3.8.2:
Uncountably Many Men / 3.8.3:
Espousable Cardinals / 3.8.4:
Finite Combinatorics with Infinite Consequences / 3.8.5:
k-critical Linear Orderings / 3.10:
Points of Departure / 3.11:
Index / 3.12:
Preface to the Second Edition
Preface to the First Edition
Graph Theory / 1:
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