On Meyniel extremal families of graphs
Combinatorics
2022-01-24 v1
Abstract
We provide new constructions of Meyniel extremal graphs, which are families of graphs with the conjectured largest asymptotic cop number. Using spanning subgraphs, we prove that there are an exponential number of new Meyniel extremal families with specified degrees. Using a linear programming problem on hypergraphs, we explore the degrees in families that are not Meyniel extremal. We give the best-known upper bound on the cop number of vertex-transitive graphs with a prescribed degree. We find new Meyniel extremal families of regular graphs with large chromatic number, large diameter, and explore the connection between Meyniel extremal graphs and bipartite graphs.
Keywords
Cite
@article{arxiv.2201.08719,
title = {On Meyniel extremal families of graphs},
author = {Anthony Bonato and Ryan Cushman and Trent G. Marbach},
journal= {arXiv preprint arXiv:2201.08719},
year = {2022}
}