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Edge-bandwidth of the triangular grid Reza Akhtar, Tao Jiang, and Dan Pritikin
 

Summary: Edge-bandwidth of the triangular grid
Reza Akhtar, Tao Jiang, and Dan Pritikin
Abstract
In 1995, Hochberg, McDiarmid, and Saks [4] proved that the vertex-bandwidth
of the triangular grid Tn is precisely n + 1; more recently Balogh, Mubayi, and
Pluh´ar [1] posed the problem of determining the edge-bandwidth of Tn. We
show that the edge-bandwidth 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 vertex-bandwidth of h is defined as
B(G, h) = max
{u,v}E(G)
|h(u) - h(v)|
and the vertex-bandwidth (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 edge-bandwidth of G
is defined as

  

Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)

 

Collections: Mathematics