Tarsi, Michael

Coloring the union of degenerate graphs ★★

Author(s): Tarsi

\begin{conjecture} The union of a $1$-degenerate graph (a forest) and a $2$-degenerate graph is $5$-colourable. \end{conjecture}


Even vs. odd latin squares ★★★

Author(s): Alon; Tarsi

A \Def{latin square} is \emph{even} if the product of the signs of all of the row and column permutations is 1 and is \emph{odd} otherwise.

\begin{conjecture} For every positive even integer $n$, the number of even latin squares of order $n$ and the number of odd latin squares of order $n$ are different. \end{conjecture}

Keywords: latin square

The additive basis conjecture ★★★

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

\begin{conjecture} For every prime $p$, there is a constant $c(p)$ (possibly $c(p)=p$) so that the union (as multisets) of any $c(p)$ bases of the vector space $({\mathbb Z}_p)^n$ contains an additive basis. \end{conjecture}

Keywords: additive basis; matrix

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