# Project Details

### Description

In 2005 the Marie Curie Fellow Janos Barat and his supervisor Carsten Thomassen made the conjecture that, for every tree T, it is possible to decompose a graph of sufficiently large edge-connectivity into copies of T. Although we could not at the time verify this for any single non-trivial instance of T, we showed that, when T is the claw, the conjecture is intimately related to Tutte's 3-flow conjecture, motivated by the classical 3-color theorem of Grotzsch.

In 2010 Carsten Thomassen obtained a breakthrough, namely a proof of the so-called weak 3-flow conjecture posed in 1988 by F.Jaeger. Among the applications, the decomposition conjecture is now verified for each star.

In 2010 Carsten Thomassen obtained a breakthrough, namely a proof of the so-called weak 3-flow conjecture posed in 1988 by F.Jaeger. Among the applications, the decomposition conjecture is now verified for each star.

Status | Finished |
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Effective start/end date | 01/01/2004 → 01/01/2014 |