It is rather a kind of general question, any hints are very pleasant to see :)
There is a chess variant called Jeson Mor: https://en.wikipedia.org/wiki/Jeson_Mor. Briefly speaking, the goal of this game for each player is to reach the central square first by his knight and leaves it in the next move.
I am trying to solve this game. My hypothesis is that black has the winning strategy applying the following intuition:
Let's reduce white and black knights only to the c1, c9 knights. If white plays c1 - d3, black plays c9 - d6 and wins, maintaining equilibirium of central square pressure. Then, since white needs to move, needs to decrease the central square pressure - any move is losing to white. If white does not play c1 - d3, black plays c3 - d6 and no move is possible to white to maintain the pressure on central square.
Generally speaking, black "copies" moves of white and wins since white is forced to move first.
Of course, the intuition can be wrong, since we consider very limited case here.
If we are supposed to convert the Jeson Mor game to the graph game, where vertices are the squares and the goal is to take the central vertex/square first and then leave it in the next move, what kind of graph theorems/branches would be useful to determine who is the winner (if any) of the game? I was thinking on some coloring graphs related things.. but not sure if it may help here.
I am rather looking for general suggestions, I know that the question is quite general, however I think I am quite stuck now :)
Thanks in advance!