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 language | English |
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Pages (from-to) | 1641-1650 |
Number of pages | 10 |
Journal | Graphs and Combinatorics |
Volume | 32 |
Issue number | 5 |
DOIs | |
Publication status | Published - Sept 2016 |
Keywords
- Local graph properties
- k-connectivity
- Lower bounds
- rigidity