Cycle space | Wikipedia audio article
Channel: wikipedia tts
Date: 03/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Cycle_space


00:00:31 1 Definitions
00:00:40 1.1 Graph theory
00:01:46 1.2 Algebra
00:04:42 1.3 Topology
00:07:19 2 Circuit rank
00:08:29 3 Cycle bases
00:09:14 3.1 Existence
00:09:56 3.2 Fundamental and weakly fundamental bases
00:11:33 3.3 Minimum weight bases
00:12:04 4 Planar graphs
00:12:13 4.1 Homology
00:13:03 4.2 Mac Lane's planarity criterion
00:13:50 4.3 Duality
00:14:40 4.4 Nowhere zero flows



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Voice name: en-AU-Wavenet-B


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SUMMARY
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In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its Eulerian subgraphs.
This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dimension of this space is the circuit rank of the graph. The same space can also be described in terms from algebraic topology as the first homology group of the graph. Using homology theory, the binary cycle space may be generalized to cycle spaces over arbitrary rings.