On-line Graph Coloring on a Bounded Board
نویسنده
چکیده
We consider a version of the on-line graph coloring problem as a two person game. Players are called Spoiler and Painter. Spoiler reveals a graph by putting or removing a node. But at each time the total number of nodes on the board is bounded by previously fixed constant n. Painter must assign a color to any new node such that two nodes connected by an edge have different colors. He cannot change colors of already colored nodes. On-line chromatic number of such game played on graphs from a class C, denoted by χC(n), is the smallest number of colors that suffices to color by Painter any graph presented by Spoiler. In this thesis we will show some lower and upper bounds of χ-number for various classes of graphs such as: forests and their generalization, t-colorable graphs, Kt-free and K1,t-free graphs.
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