On the relation of separability, bandwidth and embedding

TL;DR

This paper constructs specific bipartite graphs with small separators and large bandwidth, and shows they can be embedded as spanning subgraphs in graphs with minimum degree just over half the number of vertices.

Contribution

It introduces a new class of bipartite graphs with particular properties and demonstrates their embedding in graphs with near-half minimum degree.

Findings

Constructed bipartite graphs with small separators and large bandwidth

Proved these graphs are spanning subgraphs of graphs with minimum degree > n/2

Highlights the relationship between separability, bandwidth, and embedding

Abstract

In this paper we construct a class of bounded degree bipartite graphs with a small separator and large bandwidth. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly larger than $n/2$.