Conjecture The union of a -degenerate graph (a forest) and a -degenerate graph is -colourable.
Conjecture For every bridgeless graph there is a collection of cycles in that
- covers every edge of and
- has total length at most .
A latin square is even if the product of the signs of all of the row and column permutations is 1 and is odd otherwise.
Conjecture For every positive even integer , the number of even latin squares of order and the number of odd latin squares of order are different.
Keywords: latin square
Conjecture For every prime , there is a constant (possibly ) so that the union (as multisets) of any bases of the vector space contains an additive basis.