Is it always possible to generate a Hamiltonian circuit by adding smaller ones?
For example, a 8x8 grid can be split into four 4x4 grids, each having a Hamiltonian circuit. In this case, it is possible to combine the four circuits to make a bigger one. But is that always the case?
Also, is it necessary to have a congruent circuits to be added to make a bigger circuit? In the above example, we can find a bigger circuit by adding two 3x4 circuits, a 2x5 circuit and a 5x6 circuit also.
Note that I'm not trying to find smaller circuits in a bigger one
The above examples were randomly sketched by me, and sorry for less mathematical terms