John Asplund
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View article: Skolem Number of Cycles and Grid Graphs
Skolem Number of Cycles and Grid Graphs Open
A Skolem sequence can be thought of as a labelled path where two vertices with the same label are that distance apart. This concept has naturally been generalized to labellings of other graphs, but always using at most two of any integer l…
View article: Homebound by COVID19: The Benefits and Consequences of Non-Pharmaceutical Intervention Strategies
Homebound by COVID19: The Benefits and Consequences of Non-Pharmaceutical Intervention Strategies Open
Background . Recent research has been conducted by various countries and regions on the impact of non-pharmaceutical interventions (NPIs) on reducing the spread of COVID19. This study evaluates the tradeoffs between potential benefits (e.g…
View article: The impact of social distancing on COVID19 spread: State of Georgia case study
The impact of social distancing on COVID19 spread: State of Georgia case study Open
As the spread of COVID19 in the US continues to grow, local and state officials face difficult decisions about when and how to transition to a "new normal." The goal of this study is to project the number of COVID19 infections and resultin…
View article: Evaluating Scenarios for School Reopening Under COVID19
Evaluating Scenarios for School Reopening Under COVID19 Open
Background: Thousands of school systems have been struggling with the decisions about how to safely and effectively deliver education during the fall semester of 2020, amid the COVID19 pandemic. This study evaluates the public health impac…
View article: Homebound by COVID19: The Benefits and Consequences of Non-pharmaceutical Intervention Strategies
Homebound by COVID19: The Benefits and Consequences of Non-pharmaceutical Intervention Strategies Open
Background. Recent research has been conducted by various countries and regions on the impact of non-pharmaceutical interventions (NPIs) on reducing the spread of COVID19. This study evaluates the tradeoffs between potential benefits (e.g.…
View article: Evaluating Scenarios for School Reopening under COVID19
Evaluating Scenarios for School Reopening under COVID19 Open
Thousands of school systems have been struggling with the decisions about how to safely and effectively deliver education during the fall semester of 2020, amid the COVID19 pandemic. The objective of this study is to evaluate the public he…
View article: Homebound by COVID19: The Benefits and Consequences of Non-Pharmaceutical Intervention Strategies
Homebound by COVID19: The Benefits and Consequences of Non-Pharmaceutical Intervention Strategies Open
Objectives To evaluate the tradeoffs between potential benefits (e.g., reduction in infection spread and deaths) of non-pharmaceutical interventions for COVID19 and being homebound (i.e., refraining from community/workplace interactions). …
View article: The impact of social distancing on COVID19 spread: State of Georgia case study
The impact of social distancing on COVID19 spread: State of Georgia case study Open
As the spread of COVID19 in the US continues to grow, local and state officials face difficult decisions about when and how to transition to a “new normal.” The goal of this study is to project the number of COVID19 infections and resultin…
View article: Minimum Coprime Labelings of Generalized Petersen and Prism Graphs
Minimum Coprime Labelings of Generalized Petersen and Prism Graphs Open
A coprime labeling of a graph of order $n$ is an assignment of distinct positive integer labels in which adjacent vertices have relatively prime labels. Restricting labels to only the set $1$ to $n$ results in a prime labeling. In this pap…
View article: Minimum Coprime Labelings for Operations on Graphs
Minimum Coprime Labelings for Operations on Graphs Open
See the abstract in the attached pdf.
View article: Enclosings of Decompositions of Complete Multigraphs in $2$-Edge-Connected $r$-Factorizations
Enclosings of Decompositions of Complete Multigraphs in $2$-Edge-Connected $r$-Factorizations Open
A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is sai…
View article: Pebbling on Directed Graphs with Fixed Diameter
Pebbling on Directed Graphs with Fixed Diameter Open
Pebbling is a game played on a graph. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble r…
View article: Classification of Reconfiguration Graphs of Shortest Path Graphs With No\n Induced $4$-cycles
Classification of Reconfiguration Graphs of Shortest Path Graphs With No\n Induced $4$-cycles Open
For any graph $G$ with $a,b\\in V(G)$, a shortest path reconfiguration graph\ncan be formed with respect to $a$ and $b$; we denote such a graph as\n$S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths from\n$a$ to $b$ …
View article: The Slater and sub-k-domination number of a graph with applications to domination and k-domination
The Slater and sub-k-domination number of a graph with applications to domination and k-domination Open
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular…
View article: Using Block Designs in Crossing Number Bounds
Using Block Designs in Crossing Number Bounds Open
The crossing number ${\mbox {cr}}(G)$ of a graph $G=(V,E)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$-planar crossing number of $G$, ${\mbox {cr}}_k(G)$, is defined as the mini…
View article: ${\rm{TS}}(v,\lambda)$ with cyclic 2-intersecting Gray codes: $v\equiv 0$ or $4\pmod{12}$
${\rm{TS}}(v,\lambda)$ with cyclic 2-intersecting Gray codes: $v\equiv 0$ or $4\pmod{12}$ Open
A ${\rm{TS}}(v,\lambda)$ is a pair $(V,\mathcal{B})$ where $V$ contains $v$ points and $\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\lambda$ blocks. A $2$-block intersection graph ($2$-BIG)…
View article: ${\rm{TS}}(v,λ)$ with cyclic 2-intersecting Gray codes: $v\equiv 0$ or $4\pmod{12}$
${\rm{TS}}(v,λ)$ with cyclic 2-intersecting Gray codes: $v\equiv 0$ or $4\pmod{12}$ Open
A ${\rm{TS}}(v,λ)$ is a pair $(V,\mathcal{B})$ where $V$ contains $v$ points and $\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $λ$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\rm{…
View article: Hamiltonicity of $2$-block intersection graphs of ${\rm{TS}}(v,\lambda)$: $v\equiv 0$ or $4\pmod{12}$
Hamiltonicity of $2$-block intersection graphs of ${\rm{TS}}(v,\lambda)$: $v\equiv 0$ or $4\pmod{12}$ Open
A ${\rm{TS}}(v,\lambda)$ is a pair $(V,\mathcal{B})$ where $V$ contains $v$ points and $\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\lambda$ blocks. A $2$-block intersection graph ($2$-BIG)…
View article: On the k-planar local crossing number
On the k-planar local crossing number Open
Given a fixed positive integer $k$, the $k$-planar local crossing number of a graph $G$, denoted by $\text{LCR}_k(G)$, is the minimum positive integer $L$ such that $G$ can be decomposed into $k$ subgraphs, each of which can be drawn in a …
View article: New Perspectives on Neighborhood-Prime Labelings of Graphs
New Perspectives on Neighborhood-Prime Labelings of Graphs Open
Neighborhood-prime labeling is a variation of prime labeling. A labeling $f:V(G) \to [|V(G)|]$ is a neighborhood-prime labeling if for each vertex $v\in V(G)$ with degree greater than $1$, the greatest common divisor of the set of labels i…
View article: Pebbling on Graph Products and other Binary Graph Constructions
Pebbling on Graph Products and other Binary Graph Constructions Open
Pebbling on graphs is a two-player game which involves repeatedly moving a pebble from one vertex to another by removing another pebble from the first vertex. The pebbling number $π(G)$ is the least number of pebbles required so that, rega…
View article: $\gamma'$-Realizability and Other Musings on Inverse Domination
$\gamma'$-Realizability and Other Musings on Inverse Domination Open
We introduce and study $\gamma'$-realizable sequences. For a finite, simple graph $G$ containing no isolated vertices, $I \subseteq V(G)$ is said to be an \emph{inverse dominating set} if $I$ dominates all of $G$ and $I$ is contained by th…
View article: The k-planar crossing number of random graphs and random regular graphs
The k-planar crossing number of random graphs and random regular graphs Open
We give an explicit extension of Spencer's result on the biplanar crossing number of the Erdos-Renyi random graph $G(n,p)$. In particular, we show that the k-planar crossing number of $G(n,p)$ is almost surely $Ω((n^2p)^2)$. Along the same…
View article: Minimum Coprime Labelings for Operations on Graphs
Minimum Coprime Labelings for Operations on Graphs Open
A prime labeling of a graph of order $n$ is a labeling of the vertices with the integers $1$ to~$n$ in which adjacent vertices have relatively prime labels. A coprime labeling maintains the same criterion on adjacent vertices using any set…