The conjecture is false and it can be seen that this is so by using a computer program. For example which is not a power of two.

Alternatively we can argue as follows. For any graph we clearly have Now the bound by Alon and Spencer states In particular this implies that for any constant and large enough we have

## The conjecture is false

The conjecture is false and it can be seen that this is so by using a computer program. For example which is not a power of two.

Alternatively we can argue as follows. For any graph we clearly have Now the bound by Alon and Spencer states In particular this implies that for any constant and large enough we have