# 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 ★★★

Author(s): Alon; Tarsi

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.