2 citations · 5 across the 9 of their papers we have counts for
15 papers · 1 filter
Stability of the potential function
Catherine Erbes, Michael Ferrara, Ryan R. Martin +1
A graphic sequence is potentially -graphic if there is some realization of that contains as a subgraph. The Erdős-Jacobson-Lehel problem asks to determine ,…
Weak Dynamic Coloring of Planar Graphs
Caroline Accurso, Vitaliy Chernyshov, Leaha Hand +2
The \textit{-weak-dynamic number} of a graph is the smallest number of colors we need to color the vertices of in such a way that each vertex of degree sees a…
The Unit Acquisition Number of a Graph
Frederick Johnson, Anna Raleigh, Paul S. Wenger +1
Let 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 {\…
List-Distinguishing Cartesian Products of Cliques
Michael Ferrara, Zoltan Furedi, Sogol Jahanbekam +1
The distinguishing number of a graph , denoted , is the minimum number of colors needed to produce a coloring of the vertices of so that every nontrivial isomorphism i…
Unit Hypercube Visibility Numbers of Trees
Eric Peterson, Paul S. Wenger
A visibility representation of a graph is an assignment of the vertices of to geometric objects such that vertices are adjacent if and only if their corresponding objects a…
The List Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Poppy Immel, Paul S. Wenger
A \textit{distinguishing coloring} of a graph is a coloring of the vertices so that every nontrivial automorphism of maps some vertex to a vertex with a different color. Th…
Uniquely cycle-saturated graphs
Paul S. Wenger, Douglas B. West
Given a graph , a graph is {\it uniquely -saturated} if is not a subgraph of and adding any edge of the complement to completes exactly one copy of . In th…
Planar digraphs without large acyclic sets
Kolja Knauer, Petru Valicov, Paul S. Wenger
Given a directed graph, an acyclic set is a set of vertices inducing a subgraph with no directed cycle. In this note we show that there exist oriented planar graphs of order fo…
Saturation numbers in tripartite graphs
Eric Sullivan, Paul S. Wenger
Given graphs and , a subgraph is an -saturated subgraph of if , but for all . The saturation n…
Graph Saturation in Multipartite Graphs
Michael Ferrara, Michael S. Jacobson, Florian Pfender +1
Let be a fixed graph and let be a family of graphs. A subgraph of is -saturated if no member of is a subgraph of , but fo…
Extending Precolorings to Distinguish Group Actions
Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2
Given a group acting on a set , a -coloring of is distinguishing with respect to if the only that fixes is the identity action.…
On the approximate shape of degree sequences that are not potentially -graphic
Catherine Erbes, Michael Ferrara, Ryan R. Martin +1
A sequence of nonnegative integers is {\it graphic} if it is the degree sequence of some graph . In this case we say that is a \textit{realization} of , and we write…
On the Sum Neccesary to Ensure that a Degree Sequence is Potentially H-Graphic
Michael Ferrara, Timothy D. LeSaulnier, Casey K. Moffatt +1
A sequence of nonnegative integers π=(d_1,d_2,...,d_n) is graphic if there is a (simple) graph G with degree sequence π. In this case, G is said to realize or be a realization of π…
List Distinguishing Parameters of Trees
Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2
A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D…
Rainbow Matchings of size δ(G) in Properly Edge-colored Graphs
Jennifer Diemunsch, Michael Ferrara, Casey Moffatt +2
A {\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(δ) such that a properly edge-colore…