4 papers
Vertex maps on graphs -- Perron-Frobenius Theory
Chris Bernhardt
The goal of this paper is to describe the connections between Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron-Frobenius theory gives result…
Generalizing the rotation interval to vertex maps on graphs
Chris Bernhardt, P. Christopher Staecker
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the…
Sharkovsky's Theorem and one-dimensional combinatorial dynamics
Chris Bernhardt
A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is…
Periods of orbits for maps on graphs homotopic to a constant map
Chris Bernhardt, Zach Gaslowitz, Adriana Johnson +1
The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic…