The Characterization of planar, 4-connected, K_{2,5}-minor-free graphs
We show that every planar, 4-connected, K2;5-minor- free graph is the square of a cycle of even length at least six.
math.CO↗
arXiv subjects
Zach Gaslowitz
Publications and source records attributed to Zach Gaslowitz.
Periods of orbits for maps on graphs homotopic to a constant map
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 orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point with period $2^k$. The second is that if $v=2^ks$ for odd $s>1$, then for all $r>s$ there exists a periodic point of minimum period $2^k r$. These results are then compared to the Sharkovsky ordering of the positive integers. (The final version of this paper will appear in the Journal of Difference Equations and Applications.)
math.DS↗