11 papers
Slow graph bootstrap percolation I: Cycles
David Fabian, Patrick Morris, Tibor Szabó
Given a fixed graph and an -vertex graph , the \emph{-bootstrap percolation process} on is defined to be the sequence of graphs , which starts with…
Graph bootstrap percolation -- a discovery of slowness
David Fabian, Patrick Morris, Tibor Szabó
Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of . Given an initial set of infected edges, the transmiss…
The maximum diameter of -dimensional simplicial complexes
Stefan Glock, Olaf Parczyk, Silas Rathke +1
For every fixed dimension and sufficiently large , we determine the maximum possible diameter of a strongly connected -dimensional simplicial complex on vertices. Thi…
The maximum diameter of 2-dimensional simplicial complexes
Olaf Parczyk, Silas Rathke, Tibor Szabó
We study a problem of Santos about the largest possible diameter of a -dimensional (abstract) simplicial complex on vertices. For dimension 2, we determine the exact value o…
Improved bounds for the minimum degree of minimal multicolor Ramsey graphs
Yamaan Attwa, Sam Mattheus, Tibor Szabó +1
We provide two novel constructions of edge-disjoint -free graphs on the same vertex set, each of which has the property that every small induced subgraph contains a co…
Slow graph bootstrap percolation III: Chain constructions
David Fabian, Patrick Morris, Tibor Szabó
For graphs , we study the extremal function which is the maximum running time (until stabilisation) of an -bootstrap percolation process on vertices. Building on…