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Home > Art, Film & Photography > Spanning Tree: Minimum Spanning Tree, Kruskal's Algorithm, Prim's Algorithm, Spanning Tree Protocol, Euclidean Minimum Spanning Tree
Spanning Tree: Minimum Spanning Tree, Kruskal's Algorithm, Prim's Algorithm, Spanning Tree Protocol, Euclidean Minimum Spanning Tree

Spanning Tree: Minimum Spanning Tree, Kruskal's Algorithm, Prim's Algorithm, Spanning Tree Protocol, Euclidean Minimum Spanning Tree


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Minimum Spanning Tree, Kruskal's Algorithm, Prim's Algorithm, Spanning Tree Protocol, Euclidean Minimum Spanning Tree, Spanning Tree, Arboricity, Kirchhoff's Theorem, Reverse-Delete Algorithm, Minimum Spanning Tree-Based Segmentation, Borvka's Algorithm, Capacitated Minimum Spanning Tree, Distributed Minimum Spanning Tree, Christofides Algorithm, Degree-Constrained Spanning Tree, Random Minimal Spanning Tree, Minimum Degree Spanning Tree, K-Minimum Spanning Tree, Tree Spanner, Uniform Spanning Tree. Excerpt: The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to cover all the edges of the graph. Example A partition of the complete bipartite graph K 4,4 into three forests, showing that it has arboricity three. The figure shows the complete bipartite graph K 4,4, with the colors indicating a partition of its edges into three forests. K 4,4 cannot be partitioned into fewer forests, because any forest on its eight vertices has at most seven edges, while the overall graph has sixteen edges, more than double the number of edges in a single forest. Therefore, the arboricity of K 4,4 is three. Arboricity as a measure of density The arboricity of a graph is a measure of how dense the graph is: graphs with many edges have high arboricity, and graphs with high arboricity must have a dense subgraph. In more detail, as any n-vertex forest has at most n-1 edges, the arboricity of a graph with n vertices and m edges is at least . Additionally, the subgraphs of any graph cannot have arboricity larger than the graph itself, or equivalently the arboricity of a graph must be at least the maximum arboricity of any of its subgraphs. Nash-Williams proved that these two facts ...


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Product Details
  • ISBN-13: 9781155494128
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 94
  • Spine Width: 6 mm
  • Weight: 150 gr
  • ISBN-10: 1155494121
  • Publisher Date: 04 May 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Minimum Spanning Tree, Kruskal's Algorithm, Prim's Algorithm, Spanning Tree Protocol, Euclidean Minimum Spanning Tree
  • Width: 229 mm


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