
A method for eternally dominating strong grids
In the eternal domination game, an attacker attacks a vertex at each tur...
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4connected planar graphs are in B_3EPG
We show that every 4connected planar graph has a B_3EPG representation...
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The Connected Domination Number of Grids
Closed form expressions for the domination number of an n × m grid have ...
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Bounds on expected propagation time of probabilistic zero forcing
Probabilistic zero forcing is a coloring game played on a graph where th...
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Routing by matching on convex pieces of grid graphs
The routing number is a graph invariant introduced by Alon, Chung, and G...
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No additional tournaments are quasirandomforcing
A tournament H is quasirandomforcing if the following holds for every s...
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2× n Grids have Unbounded AnagramFree Chromatic Number
We show that anagramfree vertex colouring a 2× n square grid requires a...
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Lions and contamination, triangular grids, and Cheeger constants
Suppose each vertex of a graph is originally occupied by contamination, except for those vertices occupied by lions. As the lions wander on the graph, they clear the contamination from each vertex they visit. However, the contamination simultaneously spreads to any adjacent vertex not occupied by a lion. How many lions are required in order to clear the graph of contamination? We give a lower bound on the number of lions needed in terms of the Cheeger constant of the graph. Furthermore, the lion and contamination problem has been studied in detail on square grid graphs by Brass et al. and Berger et al., and we extend this analysis to the setting of triangular grid graphs.
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