We derive new upper bounds on the bisection width of graphs which have a regular vertex degree. We show that the bisection
width of large 3-regular graphs with ∣V∣ vertices is at most 1/6∣V∣. For the bisection width of large 4-regular graphs we show an upper bound of 2/5 ∣V∣.
Keywords graph partitioning - bisection width - regular graphs - local improvement