Adamaszek, AnnaAnnaAdamaszekAdamaszek, MichalMichalAdamaszekMnich, MatthiasMatthiasMnichSchmidt, Jens M.Jens M.Schmidt2020-01-242020-01-242016-02-18Graphs and Combinatorics 32 : 1641-1650 (2016)http://hdl.handle.net/11420/4551We propose a conjecture regarding the lower bound for the number of edges in locally k-connected graphs and we prove it for \(k=2\). In particular, we show that every connected locally 2-connected graph is \(M_3\)-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.en1435-5914201616411650Springer NatureInformatikJournal Article10.1007/s00373-016-1686-yOther