The game of arboricity

1
The game of arboricity

• Tomasz Bartnicki (Zielona Góra)
• Jarek Grytczuk (Zielona Góra)
• Hal Kierstead (Tempe)
• EuroComb05

2
Graph coloring game
(Brams, 1981, Bodlaender, 1991)

• Players Alice and Bob

• Moves Alice and Bob color vertices alternately,
  with Alice playing first

• Main Rule at any moment of the game a partial
  coloring must be proper

• And the winner is Alice, if the whole graph has
  been colored properly
• Bob otherwise

3
and so on
What is the maximum possible game chromatic
number of a planar graph?
(Kierstead Trotter, 1994, Zhu, 2004)
4
(Ann and Ben, Max und Moritz, Jacek i Placek)
edges
acyclic
acyclically
5
?
6
Results