Casteels, Karel L,
Richter, R Bruce
(2008)
*
The bond and cycle spaces of an infinite graph.
*
Journal of Graph Theory,
59
(2).
pp. 162-176.
ISSN 1097-0118.
(doi:10.1002/jgt.20331)
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Official URL http://dx.doi.org/10.1002/jgt.20331 |

## Abstract

Bonnington and Richter defined the cycle space of an infinite graph to consist of the sets of edges of subgraphs having even degree at every vertex. Diestel and Kühn introduced a different cycle space of infinite graphs based on allowing infinite circuits. A more general point of view was taken by Vella and Richter, thereby unifying these cycle spaces. In particular, different compactifications of locally finite graphs yield different topological spaces that have different cycle spaces. In this work, the Vella-Richter approach is pursued by considering cycle spaces over all fields, not just ?2. In order to understand “orthogonality” relations, it is helpful to consider two different cycle spaces and three different bond spaces. We give an analog of the “edge tripartition theorem” of Rosenstiehl and Read and show that the cycle spaces of different compactifications of a locally finite graph are related. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 162–176, 2008

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1002/jgt.20331 |

Additional information: | number of additional authors: 1; |

Uncontrolled keywords: | infinite graphs; edge spaces; cycle spaces; bond spaces |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Stewart Brownrigg |

Date Deposited: | 07 Mar 2014 00:05 UTC |

Last Modified: | 29 May 2019 12:25 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/40465 (The current URI for this page, for reference purposes) |

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