# Thomassen, Carsten

## Partitionning a tournament into k-strongly connected subtournaments. ★★

Author(s): Thomassen

**Problem**Let be positve integer Does there exists an integer such that every -strong tournament admits a partition of its vertex set such that the subtournament induced by is a non-trivial -strong for all .

Keywords:

## Edge-disjoint Hamilton cycles in highly strongly connected tournaments. ★★

Author(s): Thomassen

**Conjecture**For every , there is an integer so that every strongly -connected tournament has edge-disjoint Hamilton cycles.

Keywords:

## Subgraph of large average degree and large girth. ★★

Author(s): Thomassen

**Conjecture**For all positive integers and , there exists an integer such that every graph of average degree at least contains a subgraph of average degree at least and girth greater than .

Keywords:

## Arc-disjoint out-branching and in-branching ★★

Author(s): Thomassen

**Conjecture**There exists an integer such that every -arc-strong digraph with specified vertices and contains an out-branching rooted at and an in-branching rooted at which are arc-disjoint.

Keywords:

## Counting 3-colorings of the hex lattice ★★

Author(s): Thomassen

**Problem**Find .

Keywords: coloring; Lieb's Ice Constant; tiling; torus

## Chords of longest cycles ★★★

Author(s): Thomassen

**Conjecture**If is a 3-connected graph, every longest cycle in has a chord.

Keywords: chord; connectivity; cycle

## The Bermond-Thomassen Conjecture ★★

**Conjecture**For every positive integer , every digraph with minimum out-degree at least contains disjoint cycles.

Keywords: cycles