Upper bounds on the bisection width of 3- and 4-regular graphs

We derive new upper bounds on the bisection width of graphs which have a regular vertex degree. We show that the bisection width of sufficiently large 3-regular graphs with |V||V| vertices is at most (16+ε)|V|, ε>0ε>0. For the bisection width of sufficiently large 4-regular graphs we show an upper bound of (25+ε)|V|, ε>0ε>0.