This would imply conjecture 50. A variant of the Dinitz Conjecture . Charlie asked what happens if instead of orthogonal, we require disjoint. L 1 and L 2 are othogonal if the ordered pairs of corresponding elements are all distinct. L 1 and L 2 are disjoint if corresponding entries are distinct.
G is k-generated if the cycle space has a basis consisting of cycles of length at least k .
The connection the other way is not so obvious. Question 55 . At the moment, I am streamlining the proof and looking at a possible generalization to fractional colorings of such graphs. I have contacted you, because Albertson thought you might be interested in the resolution of the problem. Thank you for your time.