## Hamiltonian properties of polyhedra with few 3-cuts - A survey

- Kenta Ozeki, Nicolas Van Cleemput, Carol T. Zamfirescu
- Discrete Mathematics
- 2018

@article{Ozeki20142edgeHamiltonianconnectednessO4, title={2-edge-Hamiltonian-connectedness of 4-connected plane graphs}, author={Kenta Ozeki and Petr Vr{\'a}na}, journal={Eur. J. Comb.}, year={2014}, volume={35}, pages={432-448} }

- Published 2014 in Eur. J. Comb.
DOI:10.1016/j.ejc.2013.06.033

A graph G is called 2-edge-Hamiltonian-connected if for any X ⊂ {x1x2 : x1, x2 ∈ V (G)} with 1 ≤ |X| ≤ 2, G ∪ X has a Hamiltonian cycle containing all edges in X, where G ∪ X is the graph obtained from G by adding all edges in X. In this paper, we show that every 4-connected plane graph is 2edge-Hamiltonian-connected. This result is best possible in many senses and an extension of several known results on Hamiltonicity of 4-connected plane graphs, for example, Tutte’s result saying that every 4… CONTINUE READING