2 citations · 4 across the 5 of their papers we have counts for
8 papers
On the oriented diameter of graphs with given minimum degree
Garner Cochran, Zhiyu Wang
Erdős, Pach, Pollack, and Tuza [\textit{J. Combin. Theory Ser. B, 47(1) (1989), 73-79}] proved that the diameter of a connected -vertex graph with minimum degree is at most…
Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model
Lora Bailey, Heather Smith Blake, Garner Cochran +6
Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the num…
Complexity and Enumeration in Models of Genome Rearrangement
Lora Bailey, Heather Smith Blake, Garner Cochran +8
In this paper, we examine the computational complexity of enumeration in certain genome rearrangement models. We first show that the Pairwise Rearrangement problem in the Single Cu…
Large Girth and Small Oriented Diameter Graphs
Garner Cochran
In 2015, Dankelmann and Bau proved that for every bridgeless graph of order and minimum degree there is an orientation of diameter at most . In 2016,…
A New [Combinatorial] Proof of the Commutativity of Matching Polynomials for Cycles
Garner Cochran, Corbin Groothuis, Andrew Herring +2
We prove some functional equations involving the (classical) matching polynomials of path and cycle graphs and the -matching polynomial of a cycle graph. A matching in a (finite…
A Size Condition for Diameter Two Orientable Graphs
Garner Cochran, Éva Czabarka, Peter Dankelmann +1
It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745--756] that for every simple graph of order and size at least has an orientation…
Using Block Designs in Crossing Number Bounds
John Asplund, Eva Czabarka, Gregory Clark +6
The crossing number ${\mbox {cr}}(G)$ of a graph is the smallest number of edge crossings over all drawings of in the plane. For any , the -planar crossing…
-Foldability of Words
Beth Bjorkman, Garner Cochran, Wei Gao +6
We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word…