On stability of Hamilton-connectedness under the 2-closure in claw-free graphs
Zdeněk Ryjáček, Petr Vrána · Journal of Graph Theory · 2010
We show that, in a claw-free graph, Hamilton-connectedness is preserved under the operation of local completion performed at a vertex with 2-connected neighborhood. This result proves a conjecture by Bollobás et al. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:137-151, 2011