On the bandwidth of the Kneser graph

Abstract

Let G = (V, E) be a graph on n vertices and f : V → [1, n] a one to one map of V onto the integers 1 through n.Define the bandwidth B(G) of G to be the minimum possible value of dilation(f ) over all such one to one maps f . Next define the Kneser Graph K(n, r) to be the graph with vertex set [n] r , the collection of r-subsets of an n element set, and edge set E = {vw : v, w ∈[n] r , v ∩ w = ∅}. For fixed r ≥ 4 and n → ∞ we show that *

On the Embed and Project Algorithm for the Graph Bandwidth Problem

“…Jiang et al [46] analyzed the bandwidth of Kneser graphs and provided new lower and upper bounds for this family of graphs in terms of the main graph parameters n and r. No numerical demonstration of this bound is available.…”