8 citations · 26 across the 23 of their papers we have counts for
29 papers
On the Number of Zero Forcing Minimal Forts on Trees
Nguyen Hoang Dat, Franklin H. J. Kenter
We solve a conjecture by Becker et al. (arXiv:2404.05963) on the topic of zero forcing regarding the number of minimal forts of a tree. They conjectured and we prove $\mathcal{F}_{…
Leaky Forcing: Extending Zero Forcing Results to a Fault-Tolerant Setting
Beth Bjorkman, Lei Cao, Franklin Kenter +3
We study a recent variation of zero forcing called leaky forcing. Zero forcing is a propagation process on a network whereby some nodes are initially blue with all others white. Bl…
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…
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…
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…
Sparsity of Graphs that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +5
The parameter of a graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . It is shown that the minimum number of edg…