Game Chi and Game col of planar graphs
Question: What is the maximum game chromatic number of a planar graph ? What is the maximum game colouring number of a planar graph ?
It is known [KT94] that there are planar graphs G with chi_g(G) = 8. It is also known [Z03] that every planar graph G has col_g(G) at most 17 (and hence has game chromatic number at most 17). The gap between the upper bound and the lower bound is still big. It would be interesting to improve the bounds.
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References
[KT94] H. A. Kierstead and T.Trotter, Planar graph coloring with an uncooperative partner. Journal of Graph Theory 18(1994), 569-584.
[K00] H. A. Kierstead, A simple competitive graph coloring
algorithm. J.
Combin. Theory Ser. B 78 (2000), no.
1, 57--68.