David Fabian

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20242026

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3 papers · 1 filter

math.CO2026

Graph bootstrap percolation -- a discovery of slowness

David Fabian, Patrick Morris, Tibor SzabÃ³

Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_{n}$ . Given an initial set $G \subseteq K_{n}$ of infected edges, the transmiss…

math.CO2025

Slow graph bootstrap percolation III: Chain constructions

David Fabian, Patrick Morris, Tibor SzabÃ³

For graphs $H$ , we study the extremal function $M_{H} (n)$ which is the maximum running time (until stabilisation) of an $H$ -bootstrap percolation process on $n$ vertices. Building on…

math.CO2024

Slow graph bootstrap percolation II: Accelerating properties

David Fabian, Patrick Morris, Tibor SzabÃ³

For a graph $H$ and an $n$ -vertex graph $G$ , the $H$ -bootstrap process on $G$ is the process which starts with $G$ and, at every time step, adds any missing edges on the vertices o…