758 citations
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11 papers · 1 filter
Discrete-time treatment number
N. E. Clarke, K. L. Collins, M. E. Messinger +2
We introduce the discrete-time treatment number of a graph, in which each vertex is in exactly one of three states at any given time-step: compromised, vulnerable, or treated. Our…
Product throttling for power domination
Sarah E. Anderson, Karen L. Collins, Daniela Ferrero +4
The product power throttling number of a graph is defined to study product throttling for power domination. The domination number of a graph is an upper bound for its product power…
A Simple Proof Characterizing Interval Orders with Interval Lengths between 1 and
Simona Boyadzhiyska, Garth Isaak, Ann Trenk
A poset has an interval representation if each can be assigned a real interval so that in if and only if lies completely to th…
On Hamiltonians for six-vertex models
Ben Brubaker, Andrew Schultz
In this paper, we explain a connection between a family of free-fermionic six-vertex models and a discrete time evolution operator on one-dimensional Fermionic Fock space. The fami…
Split Graphs and Nordhaus-Gaddum Graphs
Christine Cheng, Karen L. Collins, Ann Trenk
A graph G is an NG-graph if χ(G) + χ(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also expl…
Unit Interval Orders of Open and Closed Intervals
Alan Shuchat, Randy Shull, Ann Trenk
A poset is a unit OC interval order if there exists a representation that assigns an open or closed real interval of unit length to each so that $x…