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math.CO2023
Forts, (fractional) zero forcing, and Cartesian products of graphs
Thomas R. Cameron, Leslie Hogben, Franklin H. J. Kenter +2
The (disjoint) fort number and fractional zero forcing number are introduced and related to existing parameters including the (standard) zero forcing number. The fort hypergraph is…
math.CO2023
Zero Forcing on 2-connected Outerplanar Graphs
Nolan Ison, Mark Kempton, Franklin Kenter
We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always…
math.CO2023
Improved bounds on the cop number when forbidding a minor
Franklin Kenter, Erin Meger, Jérémie Turcotte
Andreae (1986) proved that the cop number of connected -minor-free graphs is bounded for every graph . In particular, the cop number is at most if contains n…