Peter Bradshaw

Peter Bradshaw
Simon Fraser University · Department of Mathematics

About

7
Publications
174
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
11
Citations
Introduction
Skills and Expertise

Publications

Publications (7)
Article
We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in particular, that the cop number of any graph with girth g $g$ and minimum degree δ $\delta $ is at least 1 g ( δ − 1 ) ⌊ g − 1 4 ⌋ $\frac{1}{g}{(\delta -1)}^{\lfloor \frac{g-1}...
Article
We show that the cop number of directed and undirected Cayley graphs on abelian groups is in O(n), where n is the number of vertices, by introducing a refined inductive method. With our method, we improve the previous upper bound on cop number for undirected Cayley graphs on abelian groups, and we establish an upper bound on the cop number of direc...
Preprint
Full-text available
We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in particular, that the cop number of any graph with girth $g$ and minimum degree $\delta$ is at least $\tfrac{1}{g}(\delta - 1)^{\lfloor \frac{g-1}{4}\rfloor}$. We establish simi...
Preprint
A theorem of E. Schmeichel and J. Mitchem states that for $n \geq 4$, every balanced bipartite graph on $2n$ vertices in which each vertex in one color class has degree greater than $\frac{n}{2}$ and each vertex in the other color class has degree at least $\frac{n}{2}$ is bipancyclic. We prove a generalization of this theorem for graph transversal...
Preprint
Full-text available
We consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal graphs, and outerplanar graphs. We also obtain improved bounds for bipartite planar and toroidal graphs. We briefly consider general graphs of bounded genus.
Preprint
Full-text available
We discuss the game of cops and robbers on abelian Cayley graphs. We improve the upper bound for cop number in the undirected case, and we give an upper bound for the directed version. We also construct Meyniel extremal families of graphs with cop number $\Theta (\sqrt{n})$.
Article
We prove that the cop number of a connected abelian Cayley graph on n vertices is bounded by 7n. This proves that H. Meyniel’s conjectured bound of O(n) for the cop number of any connected graph on n vertices holds for abelian Cayley graphs.

Network

Cited By