English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Graph burning is a discrete-time process on graphs, where vertices aresequentially burned, and burned vertices cause their neighbours to burn overtime. We consider extremal properties of this process in the new setting wherethe underlying graph is also changing at each time-step. The main focus is onthe possible densities of burning vertices when the sequence of underlyinggraphs are growing grids in the Cartesian plane, centred at the origin. If thegrids are of height and width $2cn+1$ at time $n$, then all values in $\left [\frac{1}{2c^2} , 1 \right ]$ are possible densities for the burned set. Forfaster growing grids, we show that there is a threshold behaviour: if the sizeof the grids at time $n$ is $\omega(n^{3/2})$, then the density of burnedvertices is always $0$, while if the grid sizes are $\Theta(n^{3/2})$, thenpositive densities are possible. Some extensions to lattices of arbitrary butfixed dimension are also considered.

Burning the plane: densities of the infinite Cartesian grid