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papers

Publications (13)

math.CO2021

Long path and cycle decompositions of even hypercubes

Maria Axenovich, David Offner, Casey Tompkins

We consider edge decompositions of the $n$ -dimensional hypercube $Q_{n}$ into isomorphic copies of a given graph $H$ . While a number of results are known about decomposing $Q_{n}$ into…

math.CO2019

Capture-time Extremal Cop-Win Graphs

David Offner, Kerry Ojakian

We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time…

math.CO2018

Comparing the power of cops to zombies in pursuit-evasion games

David Offner, Kerry Ojakian

We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, ca…

math.CO2022

Generalized TurÃ¡n densities in the hypercube

Maria Axenovich, Laurin Benz, David Offner +1

A classical extremal, or TurÃ¡n-type problem asks to determine $ex (G, H)$ , the largest number of edges in a subgraph of a graph $G$ which does not contain a subgraph isomorph…

math.CO2017

Cop-Win Graphs: Optimal Strategies and Corner Rank

David Offner, Kerry Ojakian

We investigate the game of cops and robber, played on a finite graph, between one cop and one robber. If the cop can force a win on a graph, the graph is called cop-win. We describ…

math.CO2021

Decompositions of even hypercubes into cycles whose length is a power of two

Samuel Gibson, David Offner

If $n$ is even, the $n$ -dimensional hypercube can be decomposed into edge-disjoint cycles of length $2^{i}$ for every value of $i$ from $2$ to $n$ .