Title: On the Barát-Thomassen-Conjecture
| Speaker: | Martin Merker |
| Affiliation: | Tehnical University of Denmark |
| Room: | MC 6486 |
Abstract: Barát and Thomassen conjectured in 2006 that for every tree T there exists a natural number k(T) such that the following holds: If G is a k(T)-edge-connected simple graph with size divisible by the size of T, then G can be edge-decomposed into subgraphs isomorphic to T. So far the conjecture has only been verified for specific classes of trees such as stars, certain bistars, and paths whose length is 3, 5, or a power of 2. Recently the conjecture was also verified for trees of diameter at most 4 and for paths of any given length. Combining the methods in these proofs, we are now able to prove the general conjecture. I will give an overview of the full proof and discuss what tools are used. Joint work with Julien Bensmail, Ararat Harutyunyan, Tien-Nam Le and Stéphan Thomassé.