Abstract
This paper studies the relaxed game chromatic number of trees and outerplanar graphs. It is proved that if G is a tree then χ g d ( G)⩽2 for d⩾2. If G is an outerplanar graph, then χ g d ( G)⩽5 for d⩾2, and χ g d ( G)⩾3 for d⩽4.
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