7367 eng reportzib 0 -- 2019-06-17 -- We consider the problem of partitioning a weighted graph into k connected components of similar weight. In particular, we consider the two classical objectives to maximize the lightest part or to minimize the heaviest part. For a partitioning of the vertex set and for both objectives, we give the first known approximation results on general graphs. Specifically, we give a $\Delta$-approximation where $\Delta$ is the maximum degree of an arbitrary spanning tree of the given graph. Concerning the edge partition case, we even obtain a 2-approximation for the min-max and the max-min problem, by using the claw-freeness of line graphs. 1438-0064 urn:nbn:de:0297-zib-73675 Ralf Borndörfer Stephan Schwartz Ziena Elijazyfer Stephan Schwartz 19-25 COMBINATORICS (For finite fields, see 11Txx) Mathematical Optimization Borndörfer, Ralf Schwartz, Stephan TOLLCONTROLOPT Applied Optimization https://opus4.kobv.de/opus4-zib/files/7367/ZR-19-25.pdf