Polynomial time algorithms for the MIN CUT problem on degree restricted trees

Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree $d$ tree can be found in $O(n(\log n)^{d - 2} )$ steps. This has applications to integrated circuit layout, in particular the layout of Weinberger arrays [41]. This also yields an algorithm for determining the black/white pebble demand of degree three trees. We also show that for degree three trees, cutwidth is identical to search number and give a forbidden subgraph characterization of degree three trees having cutwidth $k$.