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math.CO2026
A Path Variant of the Explorer Director Game on Graphs
Abigail Raz, Paddy Yang
The Explorer-Director game, first introduced by Nedev and Muthukrishnan (2008), simulates a Mobile Agent exploring a ring network with an inconsistent global sense of direction. Tw…
math.CO2025
Zero Forcing on Iterated Graph Models
Christopher Brice, Erin Meger, Nhat-Dinh Nguyen +2
Modeling how information travels throughout a network has vast applications across social sciences, cybersecurity, and graph-based neural networks. In this paper, we consider the z…
math.CO2024
Note on the union-closed sets conjecture and Reimer's average set size theorem
Kengbo Lu, Abigail Raz
The Union-Closed Sets Conjecture, often attributed to Péter Frankl in 1979, remains an open problem in discrete mathematics. It posits that for any finite family of sets $S\neq\{\…