## Abstract

Let G be an infinite family of connected graphs and let k be a positive integer. We say that k is forcing for G if for all G∈ G but finitely many, the following holds. Any { - 1 , 1 } -weighing of the edges of G for which all connected subgraphs on k edges are positively weighted implies that G is positively weighted. Otherwise, we say that it is weakly forcing for G if any such weighing implies that the weight of G is bounded from below by a constant. Otherwise we say that kcollapses for G. We classify k for some of the most prominent classes of graphs, such as all connected graphs, all connected graphs with a given maximum degree and all connected graphs with a given average degree.

Original language | English |
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Pages (from-to) | 1469-1487 |

Number of pages | 19 |

Journal | Graphs and Combinatorics |

Volume | 34 |

Issue number | 6 |

DOIs | |

State | Published - 1 Nov 2018 |

### Bibliographical note

Publisher Copyright:© 2018, Springer Japan KK, part of Springer Nature.

## Keywords

- Edge voting function
- Local-global phenomena
- Weighted graphs

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics