Year: 2016
Type: preprint
Abstract: In this article, we give conditions on a graph under which the Lovász' original bound of the graph can be improved by increasing the topological connectivity of its neighbourhood complex. We also work out conditions under which computing the topological connectivity of hom complex of a pair of graphs can be simplified. In particular, hom complex as a covariant functor acting on a double mapping cylinder of graphs is a homotopy pushout of hom complex functor applied to its subgraphs. We give applications of this result where the computation of hom complexes is simplified. Finally, we explain why double mapping cylinder of graphs does not give a satisfactory definition of homotopy pushout in the category of graphs.
Source: arXiv (Cornell University)
Authors: Goyal, Shuchita, Santhanam, Rekha
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2994878179