# Graph-colouring games

Keywords: Theory

One characteristic way in which CGT throws light on go is to provide examples of phenomena that come up in go, as viewed by the theorists, which also occur in simpler games.

To say 'simpler' begs various questions. But there are certainly 'toy models' in game theory.

It is well known how to formulate go on any finite graph, using a recursive rule set and the simple ideas generated from adjacency by transitive closure. That's a game for players Red and Blue, needing only a third colour Green for empty vertices.

Here are two graph-colouring games from Winning Ways. Assume again players Blue and Red, and initial colour Green on unclaimed vertices. We need more colours, including Pale Blue and Pale Red (Pink), and Purple

Col: A play by Blue must be at a Green or Pale Blue vertex, and correspondingly for Red. It colours adjacent Green vertices Pink and adjacent Pale Blue vertices Purple (resp. colours adjacent Green vertices Pale Blue and adjacent Pink vertices Purple).

Snort: Again, a play by Blue must be at a Green or Pale Blue vertex, and correspondingly for Red. It colours adjacent Green vertices Pale Blue and adjacent Pink vertices Purple (resp. colours adjacent Green vertices Pink and adjacent Pale Blue vertices Purple).

It is Snort, of these two, which is more like go as a game of territory (and influence). It is used in Winning Ways to introduce thermography, so that urgency is in its way already present.

Graph-colouring games last edited by Bill on November 11, 2007 - 06:11