Paper Info
Title
Sparsest cuts and concurrent flows in product graphs
Abstract
A cut [S, S] is a sparsest cut of a graph G if its cut value |S||S|/|[S, S]| is maximum (this is the reciprocal of the well-known edge-density of the cut). In the (undirected) uniform concurrent flow problem on G, between every vertex pair of G flow paths with a total flow of 1 have to be established. The objective is to minimize the maximum amount of flow through an edge (edge congestion). The minimum congestion value of the uniform concurrent flow problem on G is an upper bound for the maximum cut value of cuts in G. If both values are equal, G is called a bottleneck graph. The bottleneck properties of cartesian product graphs G × H are studied. First, a flow in G × H is constructed using optimal flows in G and H, and proven to be optimal. Secondly, two cuts are constructed in G × H using sparsest cuts of G and H. It is shown that one of these cuts is a sparsest cut of G × H. As a consequence, we can prove that G × H is (not) a bottleneck graph if both G and H are (not) bottleneck graphs.
Year
DOI
Venue
2004
10.1016/S0166-218X(03)00439-6
Discrete Applied Mathematics
Keywords
Field
DocType
cartesian product,upper bound
Cut,Discrete mathematics,Bottleneck,Combinatorics,Vertex (geometry),Upper and lower bounds,Cartesian product,Minimum cut,Graph product,Mathematics,Maximum cut
Journal
Volume
Issue
ISSN
136
2-3
0166-218X
Citations 
PageRank 
References 
5
0.50
5
Authors
1
Name
Order
Citations
PageRank
Paul Bonsma128720.46