14 papers · 1 filter
Class-uniformly resolvable designs with all but one block having size two
Karen Cordova, Alexander J. Diesl, Micaela Roth +1
A Class-Uniformly Resolvable Design (CURD) is a resolvable design in which each parallel class has the same block structure. We study CURDS in which each parallel class contains on…
Discrete-time treatment number of binary trees
Karen L. Collins, Margaret-Ellen Messinger, Ann N. Trenk
The discrete-time treatment number of a graph , denoted by , was introduced in arXiv:2408.0531(3) and arises from a deterministic process in which each vertex is assigned…
Color -switches and neighborhood -balanced graphs with colors
Karen L. Collins, Jonelle Hook, Cayla McBee +1
This paper examines vertex colorings of graphs with constraints on the distribution of colors in vertex neighborhoods. We introduce color 2-switches and color degree matrices. The…
Closed Neighborhood Balanced Coloring of Graphs
K. L. Collins, M. Bowie, N. B. Fox +7
A coloring of the vertex set of a graph using the colors red and blue is a closed neighborhood balanced coloring if for each vertex there are an equal number of red and blue vertic…
The 2-burning number of a graph
C. B. Jacobs, M. E. Messinger, A. N. Trenk
We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar…
The Hereditary Closure of the Unigraphs
Michael D. Barrus, Ann N. Trenk, Rebecca Whitman
A graph with degree sequence is a \emph{unigraph} if it is isomorphic to every graph that has degree sequence . The class of unigraphs is not hereditary and in this paper we…