Lower bounds for locally highly connected graphs

Publikationstyp
Journal Article
Publikationsdatum
2016-02-18
Sprache
English
Author
Adamaszek, Anna 
Adamaszek, Michal 
Mnich, Matthias orcid-logo
Schmidt, Jens M. orcid-logo
TORE-URI
http://hdl.handle.net/11420/4551
Enthalten in
Graphs and combinatorics 
Volume
32
Start Page
1641
End Page
1650
Citation
Graphs and Combinatorics 32 : 1641-1650 (2016)
Publisher DOI
10.1007/s00373-016-1686-y
Publisher
Springer Nature
We 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.
DDC Class
004: Informatik