The Effect of Local Majority on Global Majorityin Connected Graphs

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1469-1487
Number of pages19
JournalGraphs and Combinatorics
Issue number6
StatePublished - 1 Nov 2018

Bibliographical note

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


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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