# Payan, Charles

## Stable set meeting all longest directed paths. ★★

Author(s): Laborde; Payan; Xuong N.H.

\begin{conjecture} Every digraph has a stable set meeting all longest directed paths \end{conjecture}

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## Three-chromatic (0,2)-graphs ★★

Author(s): Payan

\begin{question} Are there any (0,2)-graphs with chromatic number exactly three? \end{question}

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## 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