Year: 2015
Type: preprint
Abstract: A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper is to show that in several of the instantiations of the above approach, the quantitative bounds that were obtained are essentially best possible. These results are obtained as corollaries of a new family of graphs, which we construct by picking random subgraphs of the hypercube, and analyze using (simple) arguments from the theory of metric embedding.
Source: arXiv (Cornell University)
Authors: Moshkovitz, Guy, Shapira, Asaf
Institution: Tel Aviv University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G772833867
OpenAlex ID: W4297831671