## Factors and Factorizations of Graphs: Proof Techniques in Factor TheoryThis book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization. |

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### Contents

1 Basic Terminology | 1 |

2 Matchings and 1Factors | 15 |

3 Regular Factors and fFactors | 69 |

4 g fFactors and a bFactors | 142 |

5 a bFactorizations | 193 |

6 Parity Factors | 219 |

7 Component Factors | 252 |

8 Spanning Trees | 295 |

337 | |

Glossary of functions | 348 |

Glossary of notation | 349 |

350 | |

### Other editions - View all

Factors and Factorizations of Graphs: Proof Techniques in Factor Theory Jin Akiyama,Mikio Kano Limited preview - 2011 |

### Common terms and phrases

1-factor 1,f)-odd factor 1,f)-odd subgraph adjacent in G assume that G b]-factors bipartite graph bipartite multigraph Claim complete graph components of G connected r-regular connected simple graph contains contradiction cubic graph cut vertex define degG_s(x degG(x denotes the number disjoint subsets edge of G edges joining eG(S eG(T factor F factor of G factor theorem following theorem G is connected G satisfies G V(G g,f)-factor graph G Hamiltonian cycle Hamiltonian path holds implies independent set induced subgraph integer iso(G Kano Katerinis Lemma Let G marriage theorem matching in G maximal maximum matching minimum spanning trees obtain odd component odd integer odd(G odd{G oddca(G order at least plane graph regular factor regular graphs S C V(G S U T saturates set of G spanning subgraph spanning tree subgraph H subgraph of G Suppose that G theorem is proved vertex set vertex subset vertices of G