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math.CO2025
Pattern Forcing (0,1)-Matrices
Lei Cao, Shen-Fu Tsai
We introduce two related notions of pattern enforcement in -matrices: -forcing and strongly -forcing, which formalize distinct ways a fixed pattern must appear wit…
math.CO2025
Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson +4
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two availabl…
math.CO2025
Fault tolerance for metric dimension and its variants
Jesse Geneson, Shen-Fu Tsai
Hernando et al. (2008) introduced the fault-tolerant metric dimension , which is the size of the smallest resolving set of a graph such that $S-\left\{s\ri…