Hourglasses and Hamilton cycles in 4‐connected claw‐free graphs
Tomáš Kaiser, Mingchu Li, Zdeněk Ryjáček, Liming Xiong · Journal of Graph Theory · 2005
Abstract We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005