Thomassé, Stéphan


Directed path of length twice the minimum outdegree ★★★

Author(s): Thomassé

\begin{conjecture} Every oriented graph with minimum outdegree $k$ contains a directed path of length $2k$. \end{conjecture}

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Antidirected trees in digraphs ★★

Author(s): Addario-Berry; Havet; Linhares Sales; Reed; Thomassé

An antidirected tree is an orientation of a tree in which every vertex has either indegree 0 or outdergree 0.

\begin{conjecture} Let $D$ be a digraph. If $|A(D)| > (k-2) |V(D)|$, then $D$ contains every antidirected tree of order $k$. \end{conjecture}

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