21 citations · 31 across the 14 of their papers we have counts for
5 papers · 1 filter
Isomorphisms and properties of TAR reconfiguration graphs for zero forcing and other -set parameters
Novi H. Bong, Joshua Carlson, Bryan Curtis +2
An -TAR (token addition/removal) reconfiguration graph has as its vertices sets that satisfy some property , with an edge between two sets if one is obtained from the other b…
The multi-robber damage number of a graph
Joshua Carlson, Meghan Halloran, Carolyn Reinhart
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robb…
Minimal Zero Forcing Sets
Boris Brimkov, Joshua Carlson
In this paper, we study minimal (with respect to inclusion) zero forcing sets. We first investigate when a graph can have polynomially or exponentially many distinct minimal zero f…
Generalizing forbidden induced subgraph characterizations of high throttling numbers
Jurgen Kritschgau, Josh Carlson
Zero forcing is a process that models the spread of information throughout a graph as white vertices are forced to turn blue using a color change rule. The idea of throttling, intr…
The Hopping Forcing Rule
Joshua Carlson, John Petrucci
Zero forcing is a combinatorial game played on graphs that can be used to model the spread of information with repeated applications of a color change rule. In general, a zero forc…