New bounds on the edge-bandwidth of triangular grids

The edge-bandwidth of a graph G is the bandwidth of the line graph of G. Determining the edge-bandwidth B′(Tn) of triangular grids Tn is an open problem posed in 2006. Previously, an upper bound and an asymptotic lower bound were found to be 3n − 1 and 3n − o(n) respectively. In this paper we provide a lower bound 3n − ⌈ n/ 2 ⌉ and show that it gives the exact values of B′(Tn) for 1 ≤ n ≤ 8 and n = 10. Also, we show the upper bound 3n − 5 for n ≥ 10

New results on edge-bandwidth

The edge-bandwidth problem is an analog of the classical bandwidth problem, in which one has to label the edges of a graph by distinct integers such that the maximum difference of labels of any two incident edges is minimized. We prove tight bounds on the edge-bandwidth of hypercube and butterfly graphs, and complete k-ary trees which extends and improves on previous known results. (C) 2003 Elsevier B.V. All rights reserved