4 papers
3-Neighbor bootstrap percolation on two-dimensional grids
Neal Bushaw, Alexander Clifton
In the -neighbor bootstrap percolation process, a vertex becomes (and remains) infected if at least three of its neighbors are infected. We say that an initial configuration of…
Rainbow Separating Path Systems
Alexander Clifton, George Kontogeorgiou, S Taruni +1
We introduce a colorful version of separating path systems, in which two edges can only be separated from each other by two paths of distinct colors. We calculate the minimum sizes…
On odd covers of cliques and disjoint unions
Calum Buchanan, Alexander Clifton, Eric Culver +5
Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order…
Trail Trap: a variant of Partizan Edge Geography
Calum Buchanan, MacKenzie Carr, Alexander Clifton +4
We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing a…