## Abstract

A cycle in a graph is a set of edges that covers each vertex an even number of times. An even cycle is cycle of even cardinality. A co cycle is a collection of edges that intersects each cycle in an even number of edges. A coeven is a co cycle or the complement of a cocycle. A bieven is a collection of edges that is both an even cycle and a coeven. The even cycles, coevens, and bievens each form a vector space over the integers modulo two when addition is defined as symmetric difference of sets. An edge is co even cyclic if it belongs to a co even C for which C - {e} is an even cycle. An edge is bieven cyclic if it belongs to a bieven. We show that any edge in a graph is either coeven cyclic or bieven cyclic.

Original language | English |
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Pages (from-to) | 91-96 |

Number of pages | 6 |

Journal | Australasian Journal of Combinatorics |

Volume | 20 |

Publication status | Published - 1999 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics