Paul S. Wenger

activity

20132018

collaborators

6 papers

math.CO2018

Stability of the potential function

Catherine Erbes, Michael Ferrara, Ryan R. Martin +1

A graphic sequence $π$ is potentially $H$ -graphic if there is some realization of $π$ that contains $H$ as a subgraph. The Erdős-Jacobson-Lehel problem asks to determine $σ (H, n)$ ,…

math.CO2018

Weak Dynamic Coloring of Planar Graphs

Caroline Accurso, Vitaliy Chernyshov, Leaha Hand +2

The \textit{ $k$ -weak-dynamic number} of a graph $G$ is the smallest number of colors we need to color the vertices of $G$ in such a way that each vertex $v$ of degree $d (v)$ sees a…

math.CO2017

The Unit Acquisition Number of a Graph

Frederick Johnson, Anna Raleigh, Paul S. Wenger +1

Let $G$ be a graph with nonnegative integer weights. A {\it unit acquisition move} transfers one unit of weight from a vertex to a neighbor that has at least as much weight. The {\…

math.CO2017

List-Distinguishing Cartesian Products of Cliques

Michael Ferrara, Zoltan Furedi, Sogol Jahanbekam +1

The distinguishing number of a graph $G$ , denoted $D (G)$ , is the minimum number of colors needed to produce a coloring of the vertices of $G$ so that every nontrivial isomorphism i…

math.CO2015

Uniquely cycle-saturated graphs

Paul S. Wenger, Douglas B. West

Given a graph $F$ , a graph $G$ is {\it uniquely $F$ -saturated} if $F$ is not a subgraph of $G$ and adding any edge of the complement to $G$ completes exactly one copy of $F$ . In th…

math.CO2013

On the approximate shape of degree sequences that are not potentially $H$ -graphic