# The *k*-section of treewidth restricted graphs

## Abstract

The bisection problem is to split a graph into two equal sized sets of vertices s.t. the number of edges between vertices of different sets is minimal. Natural extensions are to split the graph in more then two sets and allow weights on the edges. This kind of problems will be defined as embedding problems from graphs into a host graphs *H*. So structured problems will be called *H-embeddings*.

Measures related to the *mincut linear arrangement* and *optimal linear arrangement* will be defined in terms of *H*-embeddings. Here we show that these problems can be solved in polynomial time for treewidth restricted graphs. These measures will be generalized on edge weighted graphs. So we get that the first can be solved (only) in pseudo polynomial time, while the second problem can be solved in polynomial time.

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