 
Summary: Edgebandwidth of the triangular grid
Reza Akhtar, Tao Jiang, and Dan Pritikin
Abstract
In 1995, Hochberg, McDiarmid, and Saks [4] proved that the vertexbandwidth
of the triangular grid Tn is precisely n + 1; more recently Balogh, Mubayi, and
Pluh´ar [1] posed the problem of determining the edgebandwidth of Tn. We
show that the edgebandwidth of Tn is bounded above by 3n  1 and below by
3n  o(n).
1 Introduction
A labeling of the vertices of a finite graph G is a bijective map h : V (G) {1, 2, . . . , V (G)}.
The vertexbandwidth of h is defined as
B(G, h) = max
{u,v}E(G)
h(u)  h(v)
and the vertexbandwidth (or simply bandwidth) of G is defined as
B(G) = min
h
B(G, h)
in which the minimum is taken over all labelings of V (G). The edgebandwidth of G
is defined as
