### Abstract

Let G be a graph and W a subset of V(G). Let g, f : V(G) → Z be two integer-valued functions such that g(x) ≤ f(x) for all x ∈ V(G) and g(y) = f(y) (mod 2) for all y ∈ W. Then a spanning subgraph F of G is called a partial parity (g, f)-factor with respect to W if g(x) ≤ deg_{F}(x) ≤ f(x) for all x ∈ V(G) and deg_{F}(y) ≡ f(y) (mod 2) for all y ∈ W. We obtain a criterion for a graph G to have a partial parity (g, f)-factor with respect to W. Furthermore, by making use of this criterion, we give some necessary and sufficient conditions for a graph G to have a subgraph which covers W and has a certain given property.

Original language | English |
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Pages (from-to) | 501-509 |

Number of pages | 9 |

Journal | Graphs and Combinatorics |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Kano, M., & Matsuda, H. (2001). Partial parity (g, f)-factors and subgraphs covering given vertex subsets.

*Graphs and Combinatorics*,*17*(3), 501-509. https://doi.org/10.1007/PL00013412