Abstract
We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For k -degenerate graphs with maximum degree Δ , the upper bound 2 Δ + 4 k − 2 for the incidence game chromatic number is given. If Δ ≥ 5 k , we improve this bound to the value 2 Δ + 3 k − 1 . We also determine the exact incidence game chromatic number of cycles, stars and sufficiently large wheels and obtain the lower bound 3 2 Δ for the incidence game chromatic number of graphs of maximum degree Δ .
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