Verfügbarkeit: Combinatorics and graph theory | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Harris, John M. 1969- (VerfasserIn), Hirst, Jeffry L. 1957- (VerfasserIn), Mossinghoff, Michael J. 1964- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY Springer 2008
Ausgabe:	2. ed.
Schriftenreihe:	Undergraduate texts in mathematics
Schlagwörter:	Combinatorial analysis Graph theory Kombinatorik Graphentheorie Lehrbuch
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=3085406&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016724302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 381 S. Ill., graph. Darst. 235 mm x 155 mm
ISBN:	9780387797106 0387797106 9780387797113

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Datensatz im Suchindex

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adam_text	Contents Preface to the Second Edition vii Preface to the First Edition ix 1 Graph Theory 1 1.1 Introductory Concepts ....................... 2 1.1.1 Graphs and Their Relatives................. 2 1.1.2 The Basics......................... 5 1.1.3 Special Types of Graphs.................. 10 1.2 Distance in Graphs......................... 17 1.2.1 Definitions and a Few Properties.............. 18 1.2.2 Graphs and Matrices.................... 21 1.2.3 Graph Models and Distance................ 26 1.3 Trees................................. 30 1.3.1 Definitions and Examples ................. 31 1.3.2 Properties of Trees..................... 34 1.3.3 Spanning Trees....................... 38 1.3.4 Counting Trees....................... 43 1.4 Trails, Circuits, Paths, and Cycles ................. 51 1.4.1 The Bridges of Konigsberg................. 52 1.4.2 Eulerian Trails and Circuits ................ 55 1.4.3 Hamiltonian Paths and Cycles............... 60 1.4.4 Three Open Problems ................... 67 1.5 Planarity............................... 73 Contents 1.5.1 Definitions and Examples ................. 74 1.5.2 Euler s Formula and Beyond................ 78 1.5.3 Regular Polyhedra..................... 80 1.5.4 Kuratowski s Theorem................... 83 1.6 Colorings.............................. 85 1.6.1 Definitions......................... 86 1.6.2 Bounds on Chromatic Number............... 88 1.6.3 The Four Color Problem.................. 93 1.6.4 Chromatic Polynomials................... 97 1.7 Matchings.............................. 101 1.7.1 Definitions......................... 102 1.7.2 Hall s Theorem and SDRs................. 104 1.7.3 The Konig-Egervary Theorem............... 109 1.7.4 Perfect Matchings ..................... Ill 1.8 Ramsey Theory........................... 116 1.8.1 Classical Ramsey Numbers.................116 1.8.2 Exact Ramsey Numbers and Bounds............118 1.8.3 Graph Ramsey Theory...................124 1.9 References..............................126 Combinatorics 129 2.1 Some Essential Problems......................130 2.2 Binomial Coefficients........................137 2.3 Multinomial Coefficients......................144 2.4 The Pigeonhole Principle......................150 2.5 The Principle of Inclusion and Exclusion..............156 2.6 Generating Functions........................164 2.6.1 Double Decks........................166 2.6.2 Counting with Repetition..................168 2.6.3 Changing Money......................171 2.6.4 Fibonacci Numbers.....................177 2.6.5 Recurrence Relations....................181 2.6.6 Catalan Numbers......................185 2.7 Polya s Theory of Counting.....................190 2.7.1 Permutation Groups ....................191 2.7.2 Burnside s Lemma.....................196 2.7.3 The Cycle Index......................200 2.7.4 Polya s Enumeration Formula...............202 2.7.5 de Bruijn s Generalization.................209 2.8 More Numbers...........................217 2.8.1 Partitions..........................218 2.8.2 Stirling Cycle Numbers ..................227 2.8.3 Stirling Set Numbers....................231 2.8.4 Bell Numbers........................237 2.8.5 Eulerian Numbers .....................242 Contents xv 2.9 Stable Marriage........................... 248 2.9.1 The Gale-Shapley Algorithm ............... 250 2.9.2 Variations on Stable Marriage............... 255 2.10 Combinatorial Geometry...................... 264 2.10.1 Sylvester s Problem .................... 265 2.10.2 Convex Polygons...................... 270 2.11 References.............................. 277 3 Infinite Combinatorics and Graphs 281 3.1 Pigeons and Trees.......................... 282 3.2 Ramsey Revisited.......................... 285 3.3 ZFC................................. 290 3.3.1 Language and Logical Axioms............... 290 3.3.2 Proper Axioms....................... 292 3.3.3 Axiom of Choice...................... 297 3.4 The Return of der Konig...................... 301 3.5 Ordinals, Cardinals, and Many Pigeons .............. 304 3.5.1 Cardinality......................... 304 3.5.2 Ordinals and Cardinals................... 308 3.5.3 Pigeons Finished Off.................... 312 3.6 Incompleteness and Cardinals ................... 318 3.6.1 Godel s Theorems for PA and ZFC............. 318 3.6.2 Inaccessible Cardinals................... 320 3.6.3 A Small Collage of Large Cardinals............ 322 3.7 Weakly Compact Cardinals..................... 324 3.8 Infinite Marriage Problems..................... 327 3.8.1 Hall and Hall........................ 328 3.8.2 Countably Many Men ................... 330 3.8.3 Uncountably Many Men.................. 336 3.8.4 Espousable Cardinals.................... 340 3.8.5 Perfect Matchings ..................... 343 3.9 Finite Combinatorics with Infinite Consequences......... 344 3.10 fr-critical Linear Orderings..................... 347 3.11 Points of Departure......................... 348 3.12 References.............................. 352 References 355 Index 369
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author	Harris, John M. 1969- Hirst, Jeffry L. 1957- Mossinghoff, Michael J. 1964-
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physical	XV, 381 S. Ill., graph. Darst. 235 mm x 155 mm
publishDate	2008
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series2	Undergraduate texts in mathematics
spellingShingle	Harris, John M. 1969- Hirst, Jeffry L. 1957- Mossinghoff, Michael J. 1964- Combinatorics and graph theory Combinatorial analysis Graph theory Kombinatorik (DE-588)4031824-2 gnd Graphentheorie (DE-588)4113782-6 gnd
subject_GND	(DE-588)4031824-2 (DE-588)4113782-6 (DE-588)4123623-3
title	Combinatorics and graph theory
title_auth	Combinatorics and graph theory
title_exact_search	Combinatorics and graph theory
title_full	Combinatorics and graph theory John M. Harris ; Jeffry L. Hirst ; Michael J. Mossinghoff
title_fullStr	Combinatorics and graph theory John M. Harris ; Jeffry L. Hirst ; Michael J. Mossinghoff
title_full_unstemmed	Combinatorics and graph theory John M. Harris ; Jeffry L. Hirst ; Michael J. Mossinghoff
title_short	Combinatorics and graph theory
title_sort	combinatorics and graph theory
topic	Combinatorial analysis Graph theory Kombinatorik (DE-588)4031824-2 gnd Graphentheorie (DE-588)4113782-6 gnd
topic_facet	Combinatorial analysis Graph theory Kombinatorik Graphentheorie Lehrbuch
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work_keys_str_mv	AT harrisjohnm combinatoricsandgraphtheory AT hirstjeffryl combinatoricsandgraphtheory AT mossinghoffmichaelj combinatoricsandgraphtheory

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