Science, Mathematics, Board Games, Hex, Algorithms.
in vertices u, u’, v, and v’ are added to separate the boundaries X, X’, Y, and Y’, as shown below. Borrowing from the definition of degrees, it follows that deg(u) = deg(u’) = deg(v) = deg(v’) = 1. Next, consider a graph ζ (zeta), whose vertices are the corners of the hexagonal cells, and whose