On Bounds of the Bisection Width of Cubic Graphs

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

“…Clark and Entringer [6] present an upper bound of n+138 3 for the bisection width of 3-regular graphs. Kostochka and Melnikov improve this asymptotically and show an upper bound of n 4 + O( √ n log n) [16]. Recently, an upper bound of 0.198n + O(log(n)) has been proved in [27].…”

Structural Properties of Sparse Graphs

“…x and almost surely Ω(n) bisection width [67] (thus Ω(n) separators) show that this result is optimal.…”

Early evaluation of direct large-scale InfiniBand networks with adaptive routing

“…Theoretical upper bound [16] on the relative bisection bandwidth β is d−2 2C + o(1) ≈ 162,5%. Practically constructible graphs with greatest known bisection are Ramanujan graphs [22] with lower bound on bisection…”