Wow that's interesting! Learned something new today! 😍👏
King's Graphs (Graph Theory of Chess)
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May 18, 2023
0
#3
Am I right when I guess that the "one dimensional rook graph" is the complete graph K8 (from any of the 8 squares on a file or rank to any other one), and the rook's graph is then the Cartesian product K8 (x) K8?
Bishop graphs seem more complicated...(?)
Is there a name for the Knight's graphs?
Edit: I found the corresponding articles on wikipedia!
Jun 29, 2023
0
#4
A different "graph theory" approach to chess: make a graph of the openings (showing where variants lead to the same position by transposition). It will be a big graph, maybe one can disentangle / separate a little, using "characteristic moves" (captures...) avoiding that they merge soon...
I guess that many branches merge together again (after all, many of the 20x20 first & second moves by each side amount to the same), so there should be much less than 20 x 20 x 20 ... positions.
Hello. Today I'd like to share a video on king's graphs, a type of graph that represents the legal moves of a king on a chessboard. It is a really interesting application of a strong product of graphs. Please share if you like it. Have a fantastic day! https://youtu.be/H22Bt1n57Gc