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Graph theory : a problem oriented approach /
"Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in that it combines the features of a text...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Washington, D.C. :
Mathematical Association of America,
©2008.
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| Colección: | MAA textbooks.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover ; Title page ; Preface; Contents; Introduction; Path Problems; Coloring Problems; Isomorphic Graphs; Planar Graphs; Disjoint Paths; Shortest Paths; ... and More; A Basic Concepts; Equivalent Graphs; Multigraphs; Directed Graphs and Mixed Graphs; Complete Graphs; Cycle Graphs; Paths in a Graph; Open and Closed Paths; Cycles; Subgraphs; The Complement of a Graph; Degrees of Vertices; The Degree Sequence of a Graph; Regular Graphs; Connected and Disconnected Graphs; Components of a Graph; More Problems; Matrices Associated with a Graph; The Degree Sequence Algorithm; B Isomorphic Graphs.
- More ProblemsC Bipartite Graphs; Complete Bipartite Graphs; Bipartite Graphs and Matrices; Cycles in a Bipartite Graph; Cycle Theorem for Bipartite Graphs; Proof of the Cycle Theorem; More Problems; D Trees and Forests; Pruning a Tree; Directed Trees; Spanning Trees; Counting Spanning Trees; Codewords for Trees: Prufer's Method; More Problems; Three conditions; Cycles and spanning trees; E Spanning Tree Algorithms; Constructing Spanning Trees; Weighted Graphs; Minimal Spanning Trees; Prim's Algorithm; Tables for Prim's Algorithm; The Reduction Algorithm; Spanning Trees and Shortest Paths.
- Minimal Paths in a Weighted GraphMinimal Path Algorithm, first attempt; Minimal Path Algorithm, revised; Tables for Dijkstra's Algorithm; Minimal Paths in a Directed Graph; Negative Weights; More Problems; Justification of the reduction algorithm; Justification of Prim's Algorithm; Justification of Dijkstra's Algorithm; Justification of Ford's Algorithm; F Euler Paths; The Königsberg Bridge Problem; Euler Paths in Directed Graphs and Directed Multigraphs; Application of Euler Paths: State diagrams, DeBruijn sequences, and rotating wheels; More Problems; G Hamilton Paths and Cycles.
- Some Negative TestsNegative test for bipartite graphs; Subgraph Test for Hamilton paths and cycles; Positive Tests for Hamilton Cycles; The Path/Cycle Principle; Some Proofs; Proof of the Path/Cycle Principle; Proof of the Bondy-Chvatal Theorem; Proof of Dirac's Theorem; More Problems; Proof of Posa's Theorem; H Planar Graphs; Regions Formed by a Plane Diagram; Proof that K_5 is Non-Planar, Using Euler's Formula; Non-Planar Graphs and Kuratowski's Theorem; More Problems; I Independence and Covering; The Independence Numbers of a Graph; A Graph Game; Covering Sets and Covering Numbers.
- More ProblemsJ Connections and Obstructions; Internally Disjoint Paths; Edge-Disjoint Paths; Path Connection Numbers; Blocking Sets; k-Connected Graphs; Vertex Cut Sets and Vertex Cut Numbers; The vertex cut number of a graph; More Problems; K Vertex Coloring; The Vertex Coloring Number of a Graph; Vertex Coloring Theorems; Algorithm form of Vertex Coloring Theorem #3:The Upper Bound Algorithm for chi; Why the algorithm works; The Four Color Theorem; Proof of the Six Color Theorem; Proof of the Five Color Theorem; Color switch; Map Coloring; More Problems; Proof of the Four Color Theorem?