Game Coloring Number Of Planar Graphs
Posted By: Camila Farah
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Kierstead and trotter realized that this was the missing tool for bounding the game chromatic numberĪ. Proved the burr erdos conjecture for planar graphs by showing that the 2 coloring number of any planar graph is at most 761. Bounds for the game coloring number of planar graphs with a specific girth by keaitsuda maneeruk nakprasit and kittikorn nakprasit get pdf 94 kb.
It is proved that the two coloring number of any planar graph is at most nine.
We show that the game coloring number of a planar graph is at most 19. This implies that the game chromatic number of a planar graph is at most 19 which improves the previous known upper bound for the game chromatic number of planar graphs. The coloring game on planar graphs was invented by steven j. Brams and was published by gardner 2.
The game chromatic number of planar graphs was first studied by keirstead and trotter 3. Recently xuding zhu made a significance contribution in this field 1 4. Lower bounds for the game coloring number of planar graphs with given girth. In this section we consider lower bounds for the game coloring number.
First we will show the following lemma. There is a planar graph g with girth 4 such that col g g 7. Let mathrm col g g be the game coloring number of a given graph g. Define the game coloring number of a family of graphs mathcal h as mathrm col g mathcal h max mathrm col g g g in mathcal h let mathcal p k be the family of planar graphs of girth at least k.
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Edge partitions of planar graphs and their game coloring numbers. Department of applied mathematics hebei university of technology tianjin 300130. These results are applied to find the following upper bounds for the game coloring number col g g of a planar graph g. Abstract the two coloring number of graphs which was originally introduced in the study of the game chromatic number also gives an upper bound on the degenerate chromatic number as introduced by borodin.
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