Question

Show that equality cannot hold if both terms on the right-hand side are even. N(p, q;...

Show that equality cannot hold if both terms on the right-hand side are even.

N(p, q; 2) ≤ N(p−1, q; 2) + N(p, q−1; 2)

The notation is from Ramsey numbers in Graph Theory. If both N(p-1,q;2) and N(p,q-1;2) are both even numbers, then the given inequality must be N(p,q;2) < or = N(p-1,q;2) + N(p,q-1;2) - 1, which is what I am struggling to show.

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