Spanning tree (mathematics) | Wikipedia audio article

This is an audio version of the Wikipedia Article:
en.wikipedia.org/wiki/Spannin...
00:00:30 1 Applications
00:01:01 2 Definitions
00:01:31 2.1 Fundamental cycles
00:02:02 2.2 Fundamental cutsets
00:02:33 2.3 Spanning forests
00:03:03 3 Counting spanning trees
00:03:34 3.1 In specific graphs
00:04:04 3.2 In arbitrary graphs
00:04:35 3.3 Deletion-contraction
00:05:06 3.4 Tutte polynomial
00:05:36 4 Algorithms
00:05:52 4.1 Construction
00:06:22 4.2 Optimization
00:06:53 4.3 Randomization
00:07:24 4.4 Enumeration
00:07:54 5 In infinite graphs
00:08:25 6 In directed multigraphs
00:08:55 7 See also
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SUMMARY
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In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (but see Spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself).