On bandwidth, cutwidth, and quotient graphs

On Bandwidth, Cutwidth, and Quotient Graphs

The bandwidth and the cutwidth are fundamental parameters which can give indications on the complexity of many problems described in terms of graphs. In this paper, we present a method for nding general upper bounds for the bandwidth and the cutwidth of a given graph from those of any of its quotient graphs. Moreover, general lower bounds are obtained by using vertex-and edge-bisection notions....

Graphs with small bandwidth and cutwidth

We give counter-examples to the following conjecture which arose in the study of small bandwidth graphs. “For a graph G, suppose that IV(G’)( < 1 + ci . diameter (G’) for any connected subgraph G’ of G, and that G does not contain any refinement of the complete binary tree of cz levels. Is it true that the bandwidth of G can be bounded above by a constant c depending only on c, and c,?” On the ...

On the bandwidth of Mobius graphs

Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.

A Note on Strongly Quotient Graphs

Cutwidth and degeneracy of graphs

We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.