Lower bounds for locally highly connected graphs

Anna Adamaszek, Michal Adamaszek, Matthias Mnich, Jens M. Schmidt

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We propose a conjecture regarding the lower bound for the number of edges in locally k-connected graphs and we prove it for k=2k=2 . In particular, we show that every connected locally 2-connected graph is M3M3 -rigid. For the special case of surface triangulations, this fact was known before using topological methods. We generalize this result to all locally 2-connected graphs and give a purely combinatorial proof. Our motivation to study locally k-connected graphs comes from lower bound conjectures for flag triangulations of manifolds, and we discuss some more specific problems in this direction.
Original languageEnglish
Pages (from-to)1641-1650
Number of pages10
JournalGraphs and Combinatorics
Volume32
Issue number5
DOIs
Publication statusPublished - Sep 2016

Keywords

  • Local graph properties
  • k-connectivity
  • Lower bounds
  • rigidity

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