3 citations · 8 across the 14 of their papers we have counts for
15 papers
Hypercups: Flipping Cups With More Than Two Sides
Micah Dykhuis, Lauren Keough, Sydney Lipton
In their 2010 article entitled ``How to invert cups at a time" in Mathematics Today, Man-Keung Siu and Ian Stewart extend a classic trick in which cups are flipped …
Triangle-degree and triangle-distinct graphs
Zhanar Berikkyzy, Beth Bjorkman, Heather Smith Blake +5
Let be a simple graph and be a vertex of . The triangle-degree of in is the number of triangles that contain . While every graph has at least two vertices wit…
Symmetry Parameters of Various Hypercube Families
Debra Boutin, Sally Cockburn, Lauren Keough +2
In this paper we study the symmetry parameters determining number, distinguishing number, and cost of 2-distinguishing, for some variations on hypercubes, namely Hamming graphs, po…
Symmetry Parameters for Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
The Mycielskian construction, denoted , takes a finite simple graph to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielsk…
Determining Number and Cost of Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A set of vertices is a determining set for a graph if every automorphism of is uniquely determined by its action on . The size of a smallest determining set for …
Distinguishing Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A graph is -distinguishable if there is a coloring of the vertices with colors so that only the trivial automorphism preserves the color classes. The smallest such i…
An Extremal Problem for the Neighborhood Lights Out Game
Lauren Keough, Darren Parker
Neighborhood Lights Out is a game played on graphs. Begin with a graph and a vertex labeling of the graph from the set for . The game…
Independent Sets in n-vertex k-chromatic, \ell-connected graphs
John Engbers, Lauren Keough, Taylor Short
We study the problem of maximizing the number of independent sets in -vertex -chromatic -connected graphs. First we consider maximizing the total number of independent…
Maximizing 2-Independent Sets in 3-Uniform Hypergraphs
Lauren Keough, A. J. Radcliffe
There has been interest recently in maximizing the number of independent sets in graphs. For example, the Kahn-Zhao theorem gives an upper bound on the number of independent sets i…
Toward a Nordhaus-Gaddum Inequality for the Number of Dominating Sets
Lauren Keough, David Shane
A dominating set in a graph is a set of vertices such that every vertex of is either in or is adjacent to a vertex in . Nordhaus-Gaddum inequailties relate a gra…
A Note on the Maximum Rectilinear Crossing Number of Spiders
Joshua Fallon, Kirsten Hogenson, Lauren Keough +3
The maximum rectilinear crossing number of a graph is the maximum number of crossings in a good straight-line drawing of in the plane. In a good drawing any two edges inter…
-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…
Extremal Threshold Graphs for Matchings and Independent Sets
L. Keough, A. J. Radcliffe
Many extremal problems for graphs have threshold graphs as their extremal examples. For instance the current authors proved that for fixed , among all graphs on vertice…
The Avalanche Polynomial of a Graph
Demara Austin, Megan Chambers, Rebecca Funke +2
The (univariate) avalanche polynomial of a graph, introduced by Cori, Dartois and Rossin in 2006, captures the distribution of the length of (principal) avalanches in the abelian s…
Graphs with the Fewest Matchings
L. Keough, A. J. Radcliffe
In recent years there has been increased interest in extremal problems for "counting" parameters of graphs. For example, the Kahn-Zhao theorem gives an upper bound on the number of…