# Havet, Frédéric

## Erdős-Posa property for long directed cycles ★★

**Conjecture**Let be an integer. For every integer , there exists an integer such that for every digraph , either has a pairwise-disjoint directed cycles of length at least , or there exists a set of at most vertices such that has no directed cycles of length at least .

Keywords:

## 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.

**Conjecture**Let be a digraph. If , then contains every antidirected tree of order .

Keywords:

## Good Edge Labelings ★★

Author(s): Araújo; Cohen; Giroire; Havet

**Question**What is the maximum edge density of a graph which has a good edge labeling?

We say that a graph is *good-edge-labeling critical*, if it has no good edge labeling, but every proper subgraph has a good edge labeling.

**Conjecture**For every , there is only a finite number of good-edge-labeling critical graphs with average degree less than .

Keywords: good edge labeling, edge labeling