Originator: Wayne Goddard (presented by Gexin Yu- REGS 2007)
Definition: A graph is k-ordered if for any k vertices in a specified order, there is a cycle that visits those vertices in that order (and possibly others). It is k-ordered Hamiltonian if there is always a spanning cycle with this property.
Background: Every 4-connected planar triangulation is Hamiltonian [Whitney]. Every 4-connected planar triangulation is 4-ordered [G].
Question: Is it true that every 4-connected planar triangulation is 4-ordered Hamiltonian?
References:
[G] Goddard, Wayne 4-connected maximal planar graphs are 4-ordered. Discrete Math. 257 (2002), no. 2-3, 405-410.