## Cycles and Spanning Trees in Cubic Graphs |

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### Contents

Divisibility of the Cycle Number | 4 |

The Minimal Cycle Number | 10 |

Properties of Cycles in Cubic | 18 |

5 other sections not shown

### Common terms and phrases

2-connected cubic graphs adjacency matrix adjacent edges basis elements Choose an edge clique graph Consider containing the edge cotree edge cycle basis cycle number cycle of length cycle space cycles in L(G disjoint cycles edge f edge is adjoined edge of G edge-connectivity endvertices factor of increase families of cubic family of graphs Figure 26 Figure 38 Figure 42 formulae four 4-cycles G which contain Gerhard Ringel graph G graph homeomorphic graph in Figure illustration in Figure include the edge increases the number isomorphic to H Lemma maximum number minimum minimum number multiple edges nonseparable cubic graph number of cycles number of spanning p-2 vertices path Proof regular graphs second illustration sequence shown in Figure spanning forests spanning trees subgraph H subgraph in Figure subgraphs isomorphic subset of spanning Theorem 6.2 theorem holds three 4-cycles tices tree of G Trees in Cubic trees in G vertex in G