Garner Cochran

collaborators

4 papers

math.CO2022

Large Girth and Small Oriented Diameter Graphs

Garner Cochran

In 2015, Dankelmann and Bau proved that for every bridgeless graph $G$ of order $n$ and minimum degree $δ$ there is an orientation of diameter at most $11 \frac{n}{δ + 1} + 9$ . In 2016,…

math.CO2018

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 $d$ -matching polynomial of a cycle graph. A matching in a (finite…

math.CO2018

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 $n \geq 5$ every simple graph of order $n$ and size at least $(2 n) - n + 5$ has an orientation…

math.CO2018

Using Block Designs in Crossing Number Bounds

John Asplund, Eva Czabarka, Gregory Clark +6

The crossing number ${\mbox {cr}}(G)$ of a graph $G = (V, E)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k \geq 1$ , the $k$ -planar crossing…