Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Edgebandwidth of the triangular grid Reza Akhtar, Tao Jiang, and Dan Pritikin
 

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 T n is precisely n+ 1; more recently Balogh, Mubayi, and
Pluh’ar [1] posed the problem of determining the edge­bandwidth of T n . We
show that the edge­bandwidth of T n 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
B # (G) = B(L(G))

  

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

 

Collections: Mathematics