The Tree Decomposition Conjecture by BarÃ¡t and Thomassen states 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 graphâ€¦ (More)

The BarÃ¡t-Thomassen conjecture asserts that for every tree T on m edges, there exists a constant kT such that every kT -edge-connected graph with size divisible by m can be edge-decomposed intoâ€¦ (More)

The Tree Decomposition Conjecture by BÃ¡rat and Thomassen states 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 graphâ€¦ (More)

An old conjecture by JÃ¼nger, Reinelt and Pulleyblank states that every 2-edgeconnected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. Weâ€¦ (More)