Game Chi of outer planar graphs

Question: What is the maximum game chromatic number of an outer planar graph ? 

It is known [KT94] that there are outer planar graphs G with chi_g(G) = 6. It is also known [GZ] that every outer planar graph G has chi_g(G) at most 7. The question is whether or not there is an outer planar graph G with chi_g(G) = 7.

References

[KT94] H. A. Kierstead and X. Zhu, Planar graph coloring with an uncooperative partner. Journal of Graph Theory 18(1994), 569-584. 

[GZ]  D. Guan and X. Zhu, Game chromatic number of outer planar graphs. Journal of Graph Theory 30(1999), 67-70.