There are lots of fun graph games: Kayles, Col, Snort, etc. When people go to play these games, how do you decide which graph to use? How does that work? Does anyone know of any good graph generators for combinatorial games?
One could consider the game
Fjords as a graph game, with some vertices
initially painted red and others blue. Then on your turn, you paint an
uncolored vertex that is adjacent to a vertex already containing your
color. This is the game you play during the second stage of Fjords.
The first stage is a longer, somewhat random process that creates the graph
and assigns the initial colors. This stage does require the players to
make decisions and is likely the "more fun" part of the game.
How else can graphs-for-games be generated? What other board games have processes like this?
A Domino-Covering Problem
3 months ago