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

Cite this

Adamaszek, A., Adamaszek, M., Mnich, M., & Schmidt, J. M. (2016). Lower bounds for locally highly connected graphs. Graphs and Combinatorics, 32(5), 1641-1650. https://doi.org/10.1007/s00373-016-1686-y