# Tarsi, Michael

## Coloring the union of degenerate graphs ★★

Author(s): Tarsi

**Conjecture**The union of a -degenerate graph (a forest) and a -degenerate graph is -colourable.

Keywords:

## Even vs. odd latin squares ★★★

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

## The additive basis conjecture ★★★

Author(s): Jaeger; Linial; Payan; Tarsi

**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.

Keywords: additive basis; matrix